“This is a story with a beginning and an end,” Elaine Mokhtefi writes in the preface to her extraordinary memoir. The title is a bit misleading – this is no dry history – but it carries something of the revolutionary optimism of her tale’s beginnings, and, in its anachronism, something too of the heartache of its ending. Because who can even talk of a first or a third world any more, rather than a whole planet of uncertainty and want, dotted here and there with well-guarded islands of cosmopolitan abundance? And who can remember anything as unitary as a capital, or as beautiful as a solidarity that doesn’t care for borders?

Mokhtefi, born Elaine Klein in prosaic Hempstead, New York, was 23 when she moved to Paris in 1951. She thought she would find something like history there – “I would drink at the fountain of the past,” she wrote – and that it would have something to do with Émile Zola and Alfred Dreyfus, Marcel Proust and Gustave Flaubert. It turned out that history wasn’t over. By 1960, when no fewer than 17 African nations announced their independence, Mokhtefi had become deeply involved with antiracist and anticolonial struggles. In France that meant agitating for Algerian independence, and against a brutal war that had already dragged on for six years.

In the process she had befriended anticolonial thinker Frantz Fanon and had fallen in love with an Algerian activist. She returned to New York that autumn and began working in the tiny apartment headquarters of the provisional government of the Algerian Republic. When independence came in the summer of 1962, she moved again, to Algiers, to be with her lover. She was, as she put it, “one of the dreamers who came to build a more perfect world”.

The challenges were enormous. The French had left trauma, stubborn hope and little else. There were only 500 university graduates in the entire country, which had a population of more than 9 million. A quarter of the populace had been confined in concentration camps. Hundreds of thousands had been killed. Throughout the 1960s, Algeria nonetheless became a beacon to the world, with “an open-door policy of aid to the oppressed”. Exiled artists, intellectuals and guerrilla fighters flocked to Algiers, representing liberation movements from the rest of Africa, Latin America, the Middle East and Southeast Asia. Mokhtefi met most of them, from South Africa’s ANC to the Viet Cong. Timothy Leary, Jean-Luc Godard, Simone de Beauvoir and Nina Simone make appearances, too.

Mokhtefi vacillates between describing herself as a participant – “We were fellow militants and the future was ours” – and a privileged observer: “I was a fly on the window, looking in, beating its wings.” She was both. She found work as assistant to the president’s press adviser, then in the national press agency and at the radio station, and finally at the university. Officially she wrote press releases and opinion pieces, organised conferences, published a magazine, wrote and directed radio shows. Unofficially, she did whatever needed to be done. When her relationship with her Algerian partner ended, Mokhtefi stayed on. “I had espoused a cause and taken the consequences,” she writes. “On a deeper level, I had found a home.”

Elaine Mokhtefi

Late one night in June 1969, her phone rang. Eldridge Cleaver, the Black Panther party’s minister of information, had landed in Algiers. After a shootout with police in California, he had been charged with attempted murder, skipped bail and fled to Cuba. He was no longer welcome there. “The Cubans dumped me,” Cleaver told Mokhtefi. His wife, Kathleen, was pregnant. He had no contacts in Algeria, or even permission to stay. “Can you help me?” he asked.

For the next three and a half years, she would be Cleaver and the Panthers’ (more would soon arrive) fixer, interpreter, comrade and co-conspirator. She had the connections and knew how to make things happen. When Cleaver wanted official recognition for the international section of the Black Panther party, she got it for them, plus monthly stipends and a villa in the hills. They called it “the Embassy”. When a German support group bought the Panthers a minibus, she picked it up from the Volkswagen plant in Hanover and ferried it to Algiers. In 1971, after Huey Newton expelled Cleaver from the Panthers, she toured the US with Kathleen, raising money for the Cleavers’ latest venture. The next year, when things were beginning to look dodgy in Algiers, she smuggled a stack of stolen US passports to a Red Army Faction contact in Frankfurt, then smuggled them back with the exiles’ photos sealed in place of the originals.

Cleaver is as charismatic and contradictory here as in his own books: by turns warm, brilliant, manipulative and ruthless. One morning in 1969 he confessed to Mokhtefi that he had killed another American fugitive, Clinton “Rahim” Smith, who, he said, had been planning to run away with the Panthers’ money. The Algerian police found Smith’s body but did not pursue the case. (She later learned that Smith was rumoured to have become involved with Kathleen.) By telling Mokhtefi, Cleaver had made her complicit in the murder; they never spoke of it again.

The authorities would be less offended by killing than by their guests’ inability to reckon with the realities of their position. The Panthers made little attempt to understand their hosts. They didn’t follow local news and interacted with few Algerians other than the women they dated. In 1972, a group of African American hijackers landed in Algeria with a million dollars in ransomed cash, and Cleaver, “vibrating to the overtones of dollar bills”, published an open letter complaining that President Houari Boumédiène had confiscated the money and abandoned their cause. The next day police raided their villa, took their weapons and cut off the phones. The crisis passed, but the message was clear: it was time to go.

For all Cleaver’s flaws, Mokhtefi writes, “I admired the man”. Her feelings ran deep. Early on the morning he left – New Year’s Day, 1973 – she drove to the Embassy to say goodbye. Cleaver, disguised in a Chesterfield coat and homburg, was sweating. “He hugged me,” she writes. She drove home “and cried uncontrollably”.

They would see each other again. One year later, Mokhtefi was deported to Paris. No explanation was given, but she had repeatedly refused the Algerian security service’s demands that she inform on a friend who had married the deposed former president Ahmed Ben Bella. Because of her political activities, she was legally not allowed to stay in France. Cleaver at this point was associating with “a swish Parisian crowd”; his glamorous photojournalist girlfriend was also sleeping with the minister of finance. Mokhtefi asked Cleaver for help. He promised to get back to her, but never did.

“I bear no grudges,” she insists, “I feel no rancour.” I believe her. Cleaver’s silence must have wounded her deeply. Algeria certainly broke her heart. The world that she and so many others struggled to create went instead in another direction. Many of her generation grew bitter in their disappointment and turned against the ideals of their youth. Mokhtefi is compassionate – true to her younger self, the people she knew and the dreams that animated her life. She is generous enough not to mention Cleaver’s later transformations into a born-again Christian, a drug addict and a Republican. She did not return to Algeria and was spared the pain of witnessing its collapse in the 1990s into civil war. She leaves us this eloquent record, written with great humility and with love.

• Algiers, Third World Capital is published by Verso. To order a copy for £14.44 (RRP £16.99) go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min p&p of £1.99.