Nico is famous as a face - a tragic beauty, the junkie Dietrich - or as the singer of three songs on the Velvet Underground's first album. Less widely known is Nico the songwriter, the serious artist who created - in partnership with ex-Velvet John Cale - two of the most extreme musical statements of the rock era. Now those albums, The Marble Index and Desertshore, have been rereleased as The Frozen Borderline: 1968-1970.

Hearing The Marble Index for the first time after knowing the singer through those three lovely tunes on The Velvet Underground and Nico is disorientating - where on earth did this harrowed sound come from? The style invented by Nico and Cale had nothing to do with everything else going on 1960s music. Centered around Nico's piercing plaint and the melancholy wheeze of her harmonium playing, it's a completely un-American sound, severed from rhythm-and-blues. Nico's debut album, Chelsea Girl, was fetching folk-tinged pop. The Marble Index is less folk than volk. It's Gothick, not in the corny white-face-and-eyeliner sense, but harking back to something pre-Christian and atavistic. Niebelungen, one of the most haunting songs on the new issue of Marble Index (albeit left off the original 1968 release), took its name from the Niebelungenlied, an 11th-century German epic poem, a heroic and tragic saga full of drowned monks and decapitations, rape and revenge.

We think of Nico as German, but although she spent much of her childhood in Germany, her parents were Spanish and Yugoslav. Depending on the account, her birthplace and birth date were either Cologne in 1938 or Budapest in 1943, while her father is variously said to have died in a concentration camp or faded away after suffering shellshock during the war. Nico herself experienced the second world war as a primal trauma, spending her earliest years sheltering from British bombing raids and witnessing the conquest of Germany by Soviet troops. She grew up as a rootless cosmopolitan (her passport read "ohne festen Wohnsitz", meaning no fixed address), receiving education in France and Italy as well as Germany, and eventually becoming fluent in seven languages. From the age of 15, she flitted across Europe (and soon between Europe and America), never staying any place for long, pursuing multiple careers as the original model-stroke-actress-stroke-singer. One minute she was in a Fellini movie, the next recording a single under the guidance of Rolling Stones manager Andrew Loog Oldham. Along the way she became the lover of the French movie star Alain Delon and had a baby son, Ari.

She was encouraged to take up songwriting by Jim Morrison, one of her many famous lovers. "He was my soul brother," Nico once said of Morrison. "He taught me to write songs. I never thought that I could, because when you come out of the fashion business ... I mean, I did a flimsy sort of writing ... He really inspired me a lot. It was like looking in a mirror then." But Nico eclipsed the Doors' darkness on The Marble Index, an album that replaces the summer of love with the winter of despair. These are the psychic landscapes, glittering in their immaculate, lifeless majesty of someone cut off from the thawing warmth of human contact and fellowship.

Along with Morrison's encouragement, a key breakthrough for Nico was her discovery of the harmonium. She liked this small instrument of Indian origin, also known as the pump organ, because it sounded "like the wind", and she developed a unique style of singing over the simple repetitive patterns she played on it. "She only had a limited command of the instrument," recalls Richard Williams, who, working at Island Records, signed Nico to record The End, effectively the final instalment of a trilogy that started with The Marble Index. "Because she played fewer notes, it restricted her singing and it became literally monotonous, but not in a pejorative way." Cale was then able "to hang interesting sounds around it" - an outlandish palette that included electric viola, glockenspiel, bells, a bosun's pipe. Her voice and harmonium were recorded first, separately; Cale would then build up textures, going through dozens of combinations. "I was pretty much left alone for two days," Cale said of the album's recording. "I let her in at the end ... and she burst into tears. 'Oh! It's so beautiful!'"

The wintry sound demanded an image change. Nico switched from dyed blonde to dark henna and started wearing black, heavy fabrics and boots. Danny Fields, her close friend and the man who got her signed to Elektra, believes it was "almost a burden to be so beautiful ... She was a very serious person and seriously wanted to be thought of a poet, a songwriter."

The Marble Index sounds like nothing before or since. If anything matches it in mood terms, it's Joy Division's Closer. Referencing the record's commercial failure, Cale said "You can't sell suicide," while Frazier Mohawk (the album's official producer) described it as not "a record you listen to. It's a hole you fall into". Yet, heroin addict and gloomy sod that she may have been, Nico appears to have been in no hurry to shuffle off this mortal coil. Indeed she clung on to life, dying in 1988 in bizarrely bathetic circumstances after tumbling off a bicycle in Ibiza.

Still, there's no doubt talk of her dark side is accurate. When Danny Fields describes her as "Nazi-esque", he's not affectionately referring to her regal, demanding personality, but to her racism. "Every once in a while there'd be something about Jews and I'd be, 'But Nico, I'm Jewish,' and she was like 'Yes, yes, I don't mean you.' She had a definite Nordic Aryan streak, [the belief] that she was physically, spiritually and creatively superior." Worse, on one occasion, she acted those beliefs out, explosively. In the restaurant at the Chelsea Hotel sometime in the very early 1970s, Nico sat with a bunch of musicians, among them a beautiful mixed-race singer who'd worked with Jimi Hendrix. According to Fields, "Nico was, I dunno, feeling neglected, or drunk, but suddenly she said 'I hate black people,' and smashed a wineglass on the table and stuck it in the girl's eye. There was lots of blood and screaming. Fortunately she just twisted it around her eye socket, so the glass never reached [the eye] but it's not like she was being cautious." Fields claims the Warhol crowd spirited Nico on to a plane and out of the country the next morning, while somehow managing to placate the victim and hush up the affair.

Exiled to Paris, Nico moved in with the avant-garde film maker Philippe Garrel and made a series of art films with him, acting and providing songs for the soundtracks. Stills from one of them, Cicatrice, adorned the sleeve of her next album, 1970's Desertshore. Setting the pattern for the rest of her career, it was recorded on a different label from its predecessor. Joe Boyd, who discovered and produced Nick Drake, was a Marble Index fan and secured her a deal with Warner/Reprise through his production company Witchseason. Cale produced again, but possibly influenced by the presence of Boyd (whose recording hallmark is restraint and naturalism) the album is less cluttered, sparer and purer, giving her voice and harmonium the spotlight.

Like The Marble Index, the music works on your mind's eye. Indeed Nico described herself as "a frustrated movie director ... I always have to see a sound, I can't listen to it only. " Lyrically, the imagery of songs like Janitor of Lunacy and Afraid is as bleak as before, but there are glimpses of tenderness. But the overwhelming impression is, again, of someone grappling with a terrible inner void. "Being around Nico was kinda depressing," recalls Boyd. "She was a very tortured character. I mean, you can see the romance of Warhol, the Factory, and the Velvets, but when you get up close up to it, you think 'Jesus, this is pretty gloomy, boring stuff.'"

Like Marble Index, Desertshore sold poorly and Nico drifted off again, recording no music for four years. In 1974, she was coaxed back into the studio by Richard Williams, who signed her and Cale to Island, to make The End. With Cale at the mixing desk, the concept was The Marble Index, Part 3. Of Nico's live rendition of The End's title track - a Doors song - Creem's Richard Cromelin memorably wrote: "If Morrison sang it as a lizard, Nico is a sightless bird, lost but ever so calm, somehow knowing the right direction. She is the pure, dead marble of a ruined Acropolis, a crumbling column on the subterranean bank of Morrison's River Styx." Playing in Berlin, Nico triggered an audience riot by performing the German national anthem Das Lied der Deutschen, (also covered on The End), complete with verses that had been banned after 1945 on account of their Nazi associations (they referred to territories ceded at Versailles and eventually seized back by Hitler). This incensed the crowd of students and hippies, who started hurling plastic seat cushions at the stage, according to Williams. "[Brian] Eno making air-raid noises on his synth, Cale pounding his piano, Nico intoning 'Deutschland, uber alles', cushions flying - it was quite something."

After her third flop in a row, Nico faded from the public eye again and recorded only two more albums before her death, neither as distinctive and remarkable as the Marble/Desertshore/End triology. But Nico's original tryptych of nihilist psalms are as enigmatic as their creator. Fields remembers her alternately as "deep", "girlish" and "bratty". "We'd be walking in New York at night and she'd have to pee, so she'd squat down between two parked cars. One time a passing cop came by and said, 'Hey, that's not very lady-like'. See, she didn't have the neuroses of babyboomer people. She didn't bother with neurosis, she went straight to psychotic. Everything was turbulent about her, starting with the bombs during her childhood. You can hear it in the words of her songs. It's a mythical thing that I think we are going to be trying to explain for a long time."

· The Frozen Borderline: 1968-1970 is out now on Rhino