At the height of their fame, the Monkees teamed up with Jack Nicholson to film the psychedelic classic Head – and destroy their careers in the process. So how do they feel about it now

Davy Jones doesn't really want to talk about Head. The former Monkees heartthrob is happy to talk about his old home in Manchester, his new home in Florida, his racehorses, his theatre career – anything, basically, except the cryptic, psychedelic art movie that, in 1968, marked the end of the Monkees' short tenure as the biggest rock band in America. "We were pawns in something we helped create but had no control over," he says crossly. "We should have made Ghostbusters, OK?"

Head could never be mistaken for Ghostbusters. It's a fourth-wall-shattering, stream-of-consciousness black comedy that mocks war, America, Hollywood, television, the music business and the Monkees themselves. These days, it is fondly remembered as one of the weirdest and best rock movies ever made, and a harbinger of the so-called New Hollywood. Quentin Tarantino and Edgar Wright are both fans. DJ Shadow and Saint Etienne have sampled its dialogue. According to director Bob Rafelson, the Beatles and the Rolling Stones both requested private screenings, while Thomas Pynchon attended a screening disguised as a plumber. But to the fans who had made the Monkees household names, it might as well never have existed. "The movie dropped like a ball of dark star," says bassist Peter Tork. "The simile of a rock in the water is too mild for how badly that movie did."

Jones, Tork and drummer Micky Dolenz are about to embark on a reunion tour but, even after 43 years, the subject of Head still stirs complicated emotions. Jones is more peevish than his cute television persona, and Tork more thoughtful than the clueless dope he portrayed. Only Dolenz is instantly recognisable as the up-and-at-'em showbiz pro. (Guitarist Mike Nesmith, who is prickly and distracted in Head, is sitting out this reunion.) Their memories of Head are as different as their personalities. "I can only give you my personal view on this," Dolenz insists. "You'll get very different answers from them. It's like Rashomon."

Rafelson, a charismatic director hungry for his big break, dreamt up a TV show about a rock band, inspired by the Beatles and especially Richard Lester's A Hard Day's Night. His business partner in the production company Raybert, Bert Schneider, was the son of the head of Columbia Pictures, whose TV division agreed a deal for the show in 1965. Putting out a call for "four insane boys," they auditioned such future stars as Harry Nilsson, Stephen Stills and Van Dyke Parks before settling on two former child actors (Jones and Dolenz) and two unknown folksingers (Nesmith and Tork).

Arriving with a bang on 12 September, 1966, The Monkees television show was the acceptable face of the counterculture, mixing cheerful anti-establishment spirit and witty, innovative direction with the old-fashioned knockabout humour of the Three Stooges and the Marx Brothers and some brilliant songs – the Neil Diamond-penned I'm a Believer kept both Good Vibrations and Strawberry Fields Forever off the top of the US charts. "The only time you saw long-haired kids on television was when they were being arrested," says Dolenz. "And then we come along and all we want to do is have fun and dance and sing and help little old ladies across the road."

Hurt by (accurate) claims that they didn't play on their own records, the band practised hard and went out on tour. Led by Nesmith, who told Dolenz the process was like Pinocchio becoming a real little boy, they seized creative control with their third album, Headquarters, and became bona fide rock stars. They hung out with the Beatles and toured with Jimi Hendrix as support. During one visit to Tork's Laurel Canyon mansion, singer Jackson Browne later recalled: "Jimi Hendrix was up there jamming with Buddy Miles in the pool house, and Peter's girlfriend was playing the drums, naked."

"When we made Headquarters, I thought I'd died and gone to heaven," says Tork. "My whole goal had been to be a member of a band that worked. The next thing I know we're making a movie and it doesn't have anything to do with the business of being in a band together."

The movie was conceived at the height of their success, but fame, Dolenz once said, "was slowly burning a hole through the centre of our brains". There is still dispute over the point of a Monkees movie. "There's some weight behind the idea that Bob and Bert wanted to wreck the Monkees, to stop it cold in its tracks," says Tork. "I've never known for sure. Bert and Bob might have thought out loud: 'Let's kill the Monkees!' Or they may have not thought so out loud but at some unconscious level, they were sick of the Monkees and wanted to do something else."

Rafelson is 78, retired and sick of interviews, but he agreed to answer a few questions via his daughter, Gabrielle. "Bob was urged by his partners and friends not to make a movie with the Monkees," Gabrielle says. "They felt he had done his work with them, and their audience was already defecting. But Bob felt he wanted to complete the cycle. He felt the truth of the Monkees story had not been told – their manipulation, protest and substantial talents. He felt the true story, in abstract [form], would be more than worth the telling."

Rafelson introduced the band to his friend, a struggling B-movie actor and screenwriter named Jack Nicholson. "Jack was fabulous," Tork says. "We adored him, all of us. Michael practically fell in love with him, in a manly sort of way." Dolenz agrees: "He was such a wonderful, charismatic, funny guy. Jack spent a lot of time with us. He hung out on the [TV] set and came out on tour, just picking up the vibe." One weekend in late 1967, they all decamped to a hotel suite in California's Ojai Valley for a brainstorming session. Amid clouds of pot smoke, they talked all weekend with the tape recorder running. Nicholson then took the tapes and turned the conversations into a screenplay; according to Rafelson, he structured it while on LSD.

Originally called Changes, the movie was retitled Head, partly as a drug reference and partly so that Raybert's next production, Easy Rider, could be marketed with the slogan "From the guys who gave you Head" – a plan torpedoed by Head's box-office nosedive. Dolenz remembers Raybert working on Easy Rider simultaneously; Nicholson, Dennis Hopper and Pete Fonda all make cameo appearances in Head, as do Frank Zappa and the former world heavyweight champion Sonny Liston. "The movie was using the Monkees to deconstruct the studio system," Dolenz reckons. "There's a scene with me and Teri Garr in the old west and I get hit by arrows and I say, 'Bob, I can't do this fake shit any more.' Well, that was a metaphor for people being fed up with the studio system."

By that stage, the Monkees were doing a good job of deconstructing themselves. The domineering Nesmith hired hard-nosed agent Jerry Perenchio and staged a walk-out over pay on the first day of the three-month shoot. While Tork, thinking it another Nesmith powerplay, ducked out, the others were wooed back with a token $1,000 each and production resumed under a cloud. "It was a joy seeing a movie being made, but I didn't like working for Bob Rafelson," Tork says. "I did what he told me, but I can't say that I ever had any heart connection with him." His favourite scene, in which he recounts what he has learned from an Indian mystic, was actually directed by Nicholson.

The first time they saw the final cut, the band weren't sure what they'd just made. "It was probably more confusing to me than it was to the average moviegoer," Tork says. "It was misunderstood by a lot of people," Dolenz says. In retrospect, the marketing seems suicidal. Posters featured the balding head of the media theorist John Brockman and the slogan: "What is Head all about? Only John Brockman's shrink knows for sure!" The so-called Monkees movie made no mention of the Monkees. "Most of our fans couldn't get in because there was an age restriction and the intelligentsia wouldn't go to see it anyway because they hated the Monkees," Dolenz says. Jones thinks Rafelson and Nicholson were just "practising their film techniques. They were throwing us to the 'gators at that point."

But Rafelson honestly believed it would work. "Bob was disappointed because he had hoped that the movie transcended the group's name," Gabrielle says. He soon realised his error. At a Greenwich Village screening, hipsters lured in by the enigmatic posters walked out the minute the Monkees appeared. The reviews were savage. Of its $790,000 budget, it recouped just $16,111.

Rafelson and Nicholson soon hit pay dirt with Easy Rider and went on to make Five Easy Pieces and other archetypal 70s films, but the band they left behind floundered. With the show over, album sales were in freefall, even though the Head soundtrack contained inspired contributions from Tork (Can You Dig It?), Nesmith (Circle Sky) and Carole King (Porpoise Song). A disillusioned Tork was the first to quit. "I didn't have a band. I wanted this kind of connection and I didn't get it, so I felt it was up to me to leave." Nesmith followed in 1970.

Tork has seen Head around 80 times but it took him years to work out why it bothered him so much. In the movie, the Monkees are hoodwinked, bamboozled, chased, assaulted, mocked, trapped in a black box and reduced to dandruff in the hair of the actor Victor Mature, before ending up back where they started. In the words of the sardonic Nicholson-penned theme tune, "So make your choice and we'll rejoice/ In never being free!"

"Most people are dazzled by the psychedelia, and that's fine, but for me finally the point of the movie is the Monkees never get out," Tork says sadly. "Which is to say Bob Rafelson's view of life is you never get out of the black box you're in. There's no escape."

So how would a Peter Tork cut of Head end?

"There might have been a scene where we get out," he says wistfully. "We jump in the water and get away."

The Monkees' 45th anniversary tour begins at the Liverpool Echo Arena on 12 May. .