Two years ago I read a strange little story in an obscure American magazine for Orthodox Jews, claiming that a descendant of Adolf Hitler had converted to Judaism and was living in Israel. I had heard rumours in Jewish circles for years about "the penitents" - children of Nazis who become Jews to try to expiate the sins of their fathers. Could it be true? I dug further and discovered that a man with a family connection to Hitler does indeed live in Israel as an Orthodox Jew. Virtually unnoticed in the English-speaking world, he was exposed seven years ago in an Israeli tabloid. Then he sank from sight. I went to Israel to meet him - and on the way I was plunged into the strange subculture of the Nazi-descended Jews.

I am walking through the alleys of the Old City of Jerusalem, to meet Aharon Shear-Yashuv. He is the son of a Nazi. And yet he was a senior rabbi in the Israeli armed forces. He lives in an apartment in the Jewish quarter, near the Western Wall. I walk through a pale gold alley; Orthodox Jewish men in long black coats and round fur hats dart past. He opens the door and looks like every other rabbi I have ever met - a black suit, a beard, a questioning shrug. He takes me into his study, settles into a chair, and says, in a thick German accent: "My father was in the Waffen-SS."

He was, he explains, born in the Ruhr Valley in 1940. During the war, his father served on the eastern front with Hitler's elite troops. What did his father do in the Waffen-SS? "I don't know," he says calmly. "When I grew up I tried to ask, but there weren't really answers."

He was four when he first met his father. "I don't remember anything about that," he says. It seems he doesn't want to talk about his father; he doesn't describe his conversion in psychological terms but in grand theological and historical ones. "During my theological studies at university it became clear that I couldn't be a minister in the church," he says. "I concluded that Christianity was paganism. One of [its] most important dogmas is that God became man, and if God becomes man then man also can become God." He pauses. "Hitler became a kind of god."

So would he have become a Jew even if the Holocaust had never happened, even if his family had been anti-Nazi? He looks surprised. "Oh yes." I try to draw him back to his father, but he seems exasperated. "Well, you see, he is a father, of course, but ideologically, there was no connection. I was so involved in my conviction that I had found the right path, all the other items no longer had any importance."

Fragments of the story begin to emerge through the haze of theological reasoning. His father was "shocked and enraged" when he went to study Judaism in America, he concedes. "For him that was the end of the world. 'My son is leaving Germany to study in a Jewish rabbinical seminary!' He told me I was crazy and renounced me as a son." When he moved to Israel, his parents pretended that it hadn't happened; they told their neighbours he was still in America. Years later, his sister arranged a meeting with his parents at a station in Düsseldorf. Shear-Yashuv arrived with a Jewish friend. His father peered out of the train, saw the Jewish stranger, and refused to get off.

Today, he believes Germany is doomed. "People there don't get married, and if they do they have one child," he says. "But the Turks and the other foreigners have many children. So it is a question of time that Germany will no longer be German." Why does he think this has happened? "I think it is a punishment for the Holocaust," he says, matter-of-factly. "Germany will leave the stage of history, no doubt about it." But the Jews, by contrast, will never die. This is a neat irony of history that he loves. "All the great cultures have left the stage of history," he says. "The Romans, the Greeks, the Egyptians, the Babylonians. But this little people, who gave so much to the world, do not." He chuckles. "That is something."

I walk through the Old City, pondering my encounter with this strange, kindly man. Something seems to be missing from his story. To stand in front of a rabbi whose father was in the SS and to hear he became a Jew because he doubted the Trinity is absurd. So I telephone Dan Bar-On, a professor of psychology at Ben Gurion University, and a world expert on the psychology of the children of perpetrators. He tells me, flatly, pitilessly: "The motive of the converts is to join the community of the victims. If you become part of the victim community, you get rid of the burden of being part of the perpetrator community." He interviewed Shear-Yashuv for his book Legacy of Silence. "For me," he says, "Shear-Yashuv represents a person who ran away from the past."

A few days later, I take a tatty bus to the Holocaust memorial Yad Vashem, on a mountain just outside Jerusalem. There is an air of absolute, manufactured silence. In the middle is a glass-and-concrete mausoleum - the memorial. I am here to meet a woman who works in the educational department. She was born in Munich, she told me on the telephone, and she is a convert. I meet her in a cafe on the terrace; it is very chichi, but the wind is blowing in from the desert. She is in her late 30s and her head is covered. Her face is stereotypically German but the mannerisms - her emphatic movements and the soaring cadences of her voice - are all Jewish.

I cannot name her, she says. (Apart from Shear-Yashuv, every convert refuses to be named.) She tells me, briskly and crossly, that although her grandparents were not perpetrators in the Holocaust, they were bystanders, anti-semites. Her mother, she explains, still says things like, "There are a lot of rich Jews in America," and her family have what she calls "a classic German narrative" about the war. She bunches her fists. "There were no Jews in these stories and no Nazis in these stories," she says. And she imitates them, angrily. "No, no, there were no Nazis, we are not Nazis. We didn't know any Jews, we didn't know anything." How did she feel about it? She pauses, and then says, "I was annoyed."

Her favoured word for Germany is "annoyed". She was "annoyed" when a synagogue recently opened in Munich. "People said, 'Now we have closed the circle; now everything is fine,'" she says. "It was like nothing had happened. But there were 11,000 Jews in Munich before the Holocaust. Where are they now?" She is annoyed by the affluence of Germany. "Everything is so clean," she says. "Everything is so ... nice. And here," she stares out over the mountains, "the life is so difficult sometimes."

Why did she become Jewish? "Because I was annoyed by how the narrative was fixed," she says. She tells me a story from the Midrash, a Jewish commentary on the Bible. There are, it states, non-Jews who are born with Jewish souls. They belong to the Jewish people, and will eventually join them. "It is only a matter of time," she says, speaking very seriously, "before you learn you should convert." I remember Shear-Yashuv said this too.

I ask her if she believes that Nazi children convert to expiate the guilt of their parents - but this angers her. "There is something not right when you do it to get rid of your German burden," she says. "That is not honest in my eyes. Do you stop being the daughter of a Wehrmacht soldier if you are Jewish? No. That is no solution. You don't get rid of it." So why is she here? "To live here, to work here, to be this bridge between two worlds." She repeats the word "bridge" and she calls it "exciting". She talks of her "motivation package" and she calls the "discourse about the Holocaust" in Germany "sophisticated". There is something emotionless about it, something deeply unsaid. And precisely on the stroke of the hour, she looks at her watch and says, "I have to go now."

I call Bar-On again. I feel the converts are giving me half-answers, scraps of answers. They talk about despising the Trinity and the terrible things that the Germans did to the Jews, but it seems like they are talking a genocide that doesn't exist, even in their memories. I can't escape the feeling that it is all about something else.

I tell Bar-On they talk obsessively about the Trinity. But is incredulity really a reason for abandoning a religion with a three-in-one god for one that still believes bushes talk and that waves are parted by the will of God? "That is another way of saying what I have already told you," he says. "They want to join the community of the victim. They may have their own way of rationalising it."

Later that day, I meet a young man. He bounces into a kebab shop on West Jerusalem's main drag. He is 24, handsome and excitable. He tells me, simply, that he hated Germany. "In Germany I didn't care about anyone," he spits. "I didn't give a fuck." He describes a jumbled youth, being thrown out of school, joining the army, rejecting the army. After a while, he drags me off to the Independence Park, sipping a Coke, and telling me how wonderful it all is in Israel.

He describes growing up in a small town in industrial western Germany. A terrible anger leaks into his sentences. When I ask him why he converted, he stares at the spindly trees, bunches his arms between his knees like an adolescent boy, and says, "I hate that question. I don't know." He calms down and says that something wasn't right for him in Germany, ever: "I was always looking for my place. I hated Catholicism. I have hated it since I was 14." He educated himself and what he likes about Judaism, he says, is that "what counts is the deed. In Christianity it is enough just to believe."

"I didn't think of my family of being like 'the Germans'," he says. "I didn't say, 'Grandfather, did you kill anyone?' My grandmother said, 'As kids under the Nazis, before the war, we had a wonderful time. They sent us to Croatia, they sent us to Sweden, and we had youth camps. How could we not be thankful for what they gave us?'" The Holocaust was just a subject you learned in history, he says. "You went in the classroom twice a week, they told you, you fell asleep."

But he tells me one of his grandmother's anecdotes about Nazism. "She remembers Kristallnacht," he says. "She was 13. She says she remembered there were Jewish shops that got burned down and it was a big loss. Because, she said, you could always go to the Jews and buy something and if you didn't have the money you could bring it in next time."

And that is his family. He never asked them about the war - I have yet to meet a convert who has. According to Bar-On, converts and their parents almost never speak about the war. He calls it the "double wall": both the parent and child erect a wall of silence; even if one tries to break it, the other will keep it firmly in place.

This man told his parents he was converting one Christmas Day. He has had death threats from neo-Nazis, he says. His hometown is full of them. Why does he think they became neo-Nazis? "Ask them - don't ask me," he replies. Did he become Jewish because of the Holocaust? "People ask me that a lot," he says, "and when I say no they don't believe me." Does he really believe that? "Maybe." He sighs and looks around at the trees. "Maybe what the war made Germany into ..." He pauses and then says, "I feel myself turning into a block of ice every time when I go back. I have to force myself to melt down again."

I call Bar-On a final time. They all say they are happy now, I tell him. Is this true? The conversion "may give them an illusion of peace", he says. "But it is not the way to work through the role of the parents [in the war]. I think it is running away from it. In order to be able to really work through the past, you have to try to understand how could it be that your father was a mass murderer. You have to think of the possibilities that had you lived at this time you might also have been able to do such things."

Is he telling me that they are always wondering what they would have done in Nazi Germany to the Jews they have become? "Being in Israel is to keep away as far as possible from it," he replies. "I am not sure to what extent they have really been accepted into Israeli society. I think they are struggling. I don't envy them."

As far as I can tell, the converts may know of each other, but they do not come together. In Judaism it is a sin to point the finger at a convert. And why would they? They are not here to be German; they are here to be Jewish.

I return to the suburbs to meet an artist. This convert is also a member of an organisation that promotes human rights for Palestinians. An incredibly beautiful woman answers the door and I say hello. "Oh, no," she says. "You are not here to speak to me - you are here to speak to my girlfriend." The woman I have come to interview is small and wiry, with short hair; she says she is 42. She speaks very, very fast. The words pour out of her.

She sits me down and gives me cake and coffee. I say I have interviewed a lot of converts. "Are they all mad?" she asks me, and laughs. What does she mean? "Well," she says, "I met some who surprised me. Some of them were shockingly unintelligent. I even wondered why they would have the intellectual independence to make this choice - especially the people who chose to be ultra-Orthodox, who chose to throw away their freedom." She shrugs. "There is stigma in conversion," she says. "People end up being fanatics."

She sips her coffee and says that she believes there is a parallel between the way that some Jews respond to the Palestinians and the way some Germans responded to the Nazis. She never asked her grandmother about the war, she says, because she loved her too much. "I was worried I would get hurt by information I didn't want to know," she says. "Sometimes I feel that a lot of Israelis live that way. It is better not to ask questions, and not be hurt, and so you don't have to look at yourself or your family or your nation. And you can live with the illusion of who is good and who is bad."

She says she was eight years old when she first heard of a Jew. "I heard a boy next door call another boy a 'stupid Jew'," she says. "I asked my mother, 'What is a Jew, and is it something bad?'"

When she learned about the Holocaust, it literally made her retch. "I was horrified by what Germans did to Jews," she says. "I was physically disgusted. And I was totally disgusted by even my own Germanness." It is strange to hear things like this over coffee in a clean apartment in the Middle East. "I didn't want to be German," she says. "And because this entered my mind so early, it became as natural as brushing my teeth."

So why did she convert? She grimaces. "It isn't rational. We are talking about religion here." But she says she ran away to Israel to convert when she was 25. And today, she berates herself for her immaturity in doing it. She was shocked by the racism in Israel. Towards her? "Towards the Arabs," she replies. "I felt that I was being told that to be a good Jew, you had to hate Arabs." So she stands at West Bank checkpoints to observe the behaviour of Israeli soldiers towards Palestinians.

"It causes a lot of tension to come here and say the things that I say," she says. So why does she say them? "Because it would be very inconsistent to have had so much criticism of Germans who were terrible cowards when it was still possible to say something, and then to come here and not speak up for justice."

She is through with Israel. She says it is because of the triple whammy of otherness - German, leftwing, gay. A shrink would say that she came here to be wrong, I tell her. "Don't think I haven't thought about it in those terms myself," she replies. "I had wanted to connect myself to a history I did not perceive as shameful. Now I am wondering if I will stay. I am more or less sure that I won't. Sometimes I feel I am not built for it, that I am not strong enough for this country." She runs her hands through her hair briskly, and shakes her head. "Sometimes I feel that just by existing I am always wrong here. But I cannot live with personal attacks now. I cannot bear it."

Later that day, I meet the man who brought me here to Israel, the man who started all this - the so-called Jewish Hitler. He is a professor at the Jewish studies faculty at one of the universities. I telephoned him, and to my surprise he answered. How could I ask: "Are you a Hitler?" I told him I was writing a story about German converts to Judaism, and he said I could come over immediately. So I go to an apartment just around the corner from where the artist lives. It is a grimy white block, with a few scrubby bushes outside.

I walk upstairs and a woman with the headscarf of all married orthodox Jewish women answers the door. She doesn't say anything, simply gestures for me to sit at a table in a room heaving with books. And then he comes in. Is this my Jewish Hitler? He is incredibly tall and slim, in a blinding yellow shirt, very animated, and his accent - an odd pulp of German, English and Hebrew - seems to zoom out of him. He is holding two pieces of paper. One is a family tree; the other is a printout of an account of the life of Alois Hitler Junior - Adolf Hitler's half-brother.

"I will tell you the whole story," he says, "on the condition that you do not print my name". He places the first piece of paper in front of me, points at names, and begins a strange, almost incomprehensible account of the lives of Germans who died more than a century ago. At the end of each summary of a long finished life, he jabs his finger on the table and says, "OK?" It only becomes clear what he is doing when I follow the tree down to a name I know - Alois Hitler.

Alois Hitler had two sons who lived to maturity - Adolf (that Adolf) and Alois Junior. This half-brother of the Führer then produced an illegitimate son called Hans. "OK?" he says. "Hans married my grandmother Erna after she divorced my grandfather."

He immediately states that he hates the Hitler branch of his family. He becomes agitated. "I have neither any blood nor DNA from Adolf and his family," he insists. "I was not socialised by that family." He met Hans only once. The Hitlers came for tea when he was 12 years old. "Hans was a very nice man," he says. "No passions, no brutality." But Erna was thrilled to have married into the Hitler clan, and remained a Nazi until she died. "I didn't know her," he says of his grandmother. "She wasn't part of my family."

The professor explains that his mother severed all connections with the Hitlers. As a teenager she was beaten for refusing to go to Hitler Youth dances, and when she gave birth to the professor - an illegitimate child she conceived during an affair with a married man - her mother and stepfather disowned her. He was raised in a series of rented rooms, while the Hitlers lived well. After the war, his grandmother changed her name, but her beliefs remained.

He begins to tell me what happened to his mother during the war. She worked as a typist for the Wehrmacht in Poland and she saw dead Jews hanging in the town squares. "She was a girl in the war," he says, "but I always appreciated that she told me the truth about it. We spoke frankly. I never heard that normal German lie you hear so often from that generation." His voice rises and he impersonates them with a fierce whine: "'We didn't know, we just did our duty.'" And he thumps the table. "My grandparents never understood what they had done," he says. "My mother understood." When she came home after the Allied victory, she was denounced as a Nazi, and the Communists seized her flat. "She became one of those German ladies who cleared up after all the bombing." He stomps to the kitchen and comes back, thrusting two silver spoons at me. "That is all that my mother brought home from the war. I keep them to honour her."

It was a brutal childhood: he barely saw his father, and his mother beat him - one time so severely that she couldn't go to work for three days because her fingers were too swollen to type. "She was a fighter," he says. "It is not the nicest thing you can be." Was she religious? He gives a deranged giggle. "She had the religion of herself," he says.

His mother was entirely alone. "Nobody helped anybody at that time," he says. His father had another family - a real family: "I saw my father very seldom and the times I saw him I was so proud to have a father that it was not the time to ask what he did in the war. He died when I was 19. So I never asked him what he did." But he does know his father was a major in the Wehrmacht. So, barring a miracle, he killed people for Hitler.

His journey towards Judaism was long. "It was not a sudden light from heaven that came down." When he was a teenager he met a girl who was interested in Judaism, and he read Mein Kampf. "I was embarrassed when I read it," he says. "How could people be so stupid as to elect a person who was writing things like this? It's awful." He blinks at me. "I don't think you can really understand how awful it is if you don't read it in German. I put it away. But I keep it here." Did he ever finish it? He scowls at me for the first and only time. "No."

When the time came for him to be conscripted into the German army, he decided to take a theology degree, because he wanted to benefit from an ironic leftover from Nazism: Hitler promised the Pope in 1933 that he wouldn't conscript priests, and the law has never been repealed. "I am a pacifist," he says. "You raise up an army if you think you have to use it." As part of the degree, he was due to spend six weeks in Israel in the early 1970s. "I felt at home. I was no longer living in a conflict. I didn't have to reject the older generation. And I thought I had met for the first time a nationality that at that point in history - today it is more problematic - still had good reasons to be proud of itself." So he stayed.

We go out on to the balcony to smoke. He really enjoys his cigarette; I can see he is a pleasure-savouring man. He does not have the heaviness of the other converts, who all seemed crushed by an invisible burden. Is it because he spoke to his mother about it all? I steel myself and ask: would he have become Jewish without the Holocaust? "I think not," he says. "The sharp distinction between the generations that committed the crimes and the generation born after wouldn't exist. Non-Germans hardly understand that a whole generation checked out our teachers and asked, 'Where were you 20 years ago?'"

And then, to my surprise, he calls his son - his Israeli son - a fascist. "When I hear my own son speak - as I did last weekend - I sat like this," and he does the Hitler salute. "Two of my sons are chauvinists and one of them is even partially racist. I can't listen to fascistic discourse. I don't suffer that." They talk about the Palestinians with contempt. "Each time I hear it is another time too much. If the Holocaust and the Third Reich have really somehow shaped me, I am a sworn democrat. I believe that democracy has to prove itself by keeping the rights of its minorities."

I have been with this man for three hours, insistently asking why - why did you convert? Why? This stray branch of the Hitler family tree stares out at his dull suburban street at the heart of the Jewish state, puffs on his cigarette, and begins to talk about the images of the Holocaust that linger in his mind. "I see that soldier trampling that child and in the end killing it, and I remember that kind of aggression. I remember the feeling of the child, too. I remember both. I could see my father or my grandfather really standing there."

And as he says this, his shoulders seem to relax. He is giving me my answer. "And all I can say, Tanya," he says from inside his little cloud of smoke, "is that since I came to Israel, that feeling isn't there any more."