The live-in customers at the Alcor Life Extension Foundation in Arizona reside in eight 10ft-high steel tanks filled with liquid nitrogen. They are incapable of breathing, thinking, walking, riding a bike or scratching an itch. But don’t refer to them as deceased.

They may be frozen at minus 320 degrees Fahrenheit and identified by prison-like numbers. But to Alcor, the 67 bodies - in many cases, just severed heads - are patients who may live again if science can just figure out how to reanimate them.

"They’re no different than a flat-lining patient who gets a defibrillator to bring them back to life," says Joseph A Waynick, Alcor’s president and chief executive. "With our patients, the only difference is the length of time."

Alcor is a small nonprofit company built on the spectacular wager that it can rescue its patients from natural post-mortem deterioration until a distant time when cellular regeneration, nanotechnology, cloning or some other science can restart their lives, as if the diseases, heart attacks, old age, murders or accidents that concluded their first goes round had never happened. It’s an idea that’s been around since the late 19th century, when Kincardine-born Sir James Dewar began his research into cryogenics.

So far, nobody has been revived. And there is little evidence that anybody ever will be. The first intentionally frozen man, James Bedford, is still here - 38 years after his official death and 20 years after he was moved from a storage facility where his family kept him frozen in liquid nitrogen. No-one has been thawed out, except for a woman whose sister successfully sued to get the body out of deep freeze.

Alcor’s most renowned frozen parts - the head and trunk of the once-mighty Ted Williams, the Boston Red Sox baseball player - are in one of the gigantic tanks. He is there despite a protracted family feud that balanced the player’s will, which stated his desire to be cremated, against a note he signed from a sickbed, which said he preferred to be frozen. The note won.

What Alcor sells is hope - if only, so far, to a small sliver of the potentially dead. But like its customers, the company is optimistic. It sees itself primarily as a research facility that looks beyond the old-fashioned post-death options of burial and cremation.

Alcor executives are convinced that cryonics will catch on someday, and they have recently stepped up the company’s marketing - inviting the public to take tours of its facility, for example - to make sure that it happens sooner rather than later.

Still, with just one site, built in an industrial area of Scottsdale, Arizona, Alcor is not yet a threat to the £8 billion-a-year business of burying or cremating the dead. The same goes for the rest of the cryonics industry. In fact, the company has only one full-service rival, the Cryonics Institute, outside Detroit, which has preserved 68 bodies, including the mother and two wives of its founder, Robert C W Ettinger, who is 86.

The service offered by these fledgling companies is not cheap. If you hand your head - or "neuro" - to Alcor, it costs £42,000; if you freeze your body, the price rises to nearly £80,000. The Cryonics Institute charges much less: £14,800 for a full body. In any case, many people who are willing to believe that their severed head can be reanimated and attached to a new body at some unknown time in the distant future are not ones to fret about costs. At Alcor, Waynick says that nearly all the future frozen buy life insurance policies to cover their fees, and designate the company as the beneficiary.

One such customer is Charlie Matthau, 39, a film director who signed up with Alcor in his late teens after reading about it in a magazine. His insurance premium, he says, "is cheaper than what I pay for parking".

Matthau, son of the actor Walter Matthau, who died in 2000 and had a traditional burial, says he recognises that cryonics is on the fringe. He asked his rabbi for religious guidance in his decision. "People believe in the most bizarre stuff," Matthau says. "It’s a long shot that probably won’t work, but it beats the alternative."

Matthau tried to persuade his father to join him in the liquid nitrogen but did not succeed. According to Matthau, his father’s view was: "I don’t want to do it because it might work and I don’t want to come back as a carnival act."

The carnival did not have to wait for a reanimation. It arrived in Scottsdale with Williams’s body in mid-2002, hyped by the subsequent revelation by a former Alcor employee that the ballplayer’s head had been separated from his body. The resulting publicity astonished the company, even though Waynick’s predecessor, Jerry Lemler, hoped at least a year in advance to capitalise on the fact that Williams would be its slugger-in-residence.

In 2001, a year before Williams died, Lemler wrote to John Henry Williams, the son of the slugger, about the "huge" impact of a "post-mortem disclosure of your dad’s becoming an Alcor member". Lemler, a psychiatrist, ended his letter by saying: "We’ve never had a .400 hitter as a member. It’s a genuine first for us."

But by the time John Henry Williams died in 2004, he had never let Alcor acknowledge that his father was in the tanks (nor will Alcor say if John Henry Williams is there) but he produced for the Florida probate court a signed, unnotarised, oil-stained note saying he, his father and his sister, Claudia, all wanted to be frozen post mortem.

But perhaps cryonics needed a sitcom, not a dead ballplayer, to bolster its profile with a sceptical public. The quirky HBO series Six Feet Under created a "comfortability for customers to speak more openly," says Robert J Biggins, the president-elect of the National Funeral Directors Association. "As dysfunctional as they were, the fact that factual information took place in a funeral home raised the comfort level."

To raise the comfort level with its services, Alcor offers tours of its facility to anyone wanting to take one. The tours include a visit to the operating room, though not when a medical team is preparing lifeless bodies for freezing by pumping them full of chemicals to protect their insides from ice formation nor when they are taking 15 minutes or so to saw off a head - technically a "cephalic isolation." The tours, however, do include a walk through the "patient bay": the banks of tanks full of bodies and heads.

Tanya Jones, Alcor’s chief operating officer, has the ready smile and willing demeanour of a hotel concierge. She wants to please, if not proselytise. Her head - and perhaps her whole body - will one day be preserved inside one of the tanks that dwarf her as she gives a tour.

"The people who do this are very optimistic about technology and believe life is worth living," she says calmly, but with subtle excitement in her voice. "If we can prove this works, everybody will know about us."

Proving that it will work, of course, will take time. Perhaps that proof is what is needed to build a larger customer base. So far, after 33 years in business, the non-guaranteed promise of a second life has yielded only 52 frozen heads, 15 gelid bodies and 721 warm-blooded, still-breathing, dues-paying members. "Our market is so vast, but our business is small," Waynick says.

Alcor is financially dependent on the timing of its members’ expiring. All will die, of course, but they don’t do so by an accounts-receivable schedule. Of its £1.2 million in revenue in 2002, one-quarter came from freezing fees from eight patients, but far more, 62 per cent, came from donors such as the estate of one Alcor "patient", Richard C Jones, whose annual royalties from the situation comedy Mama’s Family go to Alcor. The rest comes from members, who pay dues of up to £210 a year to support the foundation.

In 2003, with fewer donations and about four or five new freezees, Waynick says revenue dropped to £635,000. Financial documents were unavailable for 2004, but Waynick says there were eight new patients, or "cryosuspensions".

Most people who join Alcor were previously convinced of cryonics’ promise and are not frightened by the absence of a guarantee of awakening in the distant future, or by the grisliness of removing their heads, Waynick says. "They’ve pretty much made up their minds about doing this. For those who know cryonics, there’s no problem with us." Nor, it would seem, with the suggestion that life insurance be deployed to prepare for a second life.

These are the word-of-mouthers, life-extension advocates and the curious, who, like Charlie Matthau, want a little zing in their afterlife. Alcor knows that the rest of its potential market - that is, almost everyone else - needs an education. The company tries to do much of that on its website, www.alcor.org, a comprehensive archive of newsletters, scientific papers, patient case studies (with minute-by-minute play of their surgeries), operating-room photographs and membership documents.

But what of grabbing more of the burial-cremation market? Whose bodies and heads will reside in the tanks - with a capacity for 300 bodies or 900 heads - that will fill the new patient bay currently being built? Is waiting for true believers a valid marketing strategy?

"In a sense it should be easy to market," says Mary Roach, author of Stiff: The Curious Lives of Human Cadavers (Norton, 2003). "You’re marketing immortality." But, she says, "I find the head-freezing business a little ... over-hopeful, a little too self-absorbed."

Alcor says it is not sitting still while its potential customers are buried or turned to ashes, nor is it waiting to react to another tabloid frenzy like the Williams case. It recently completed a 30-minute documentary, which it wants to broadcast as a cable-TV infomercial and sell on DVD. It has opened its doors to local community college students who are studying mortuary science. It also hopes to expand its annual scientific conference to a wider audience.

"It’s been easy to sell the true story that this is a scientific endeavour," says Deborah Johnson, Alcor’s public relations consultant and producer of the documentary. "We think there are a tremendous number of people who might be interested in becoming members if they knew we existed."

For Waynick, the ultimate goal of Alcor’s cautiously aggressive campaign is to lure enough people away from burial and cremation to build a bigger business and prove to sceptics that medical research, not some kind of voodoo, is being performed inside the company’s pale blue stucco exterior walls. After all, with the new patient bay, and the ability to work on two patients at a time in a new operating room that is being built, there is plenty of room to capitalise on Alcor’s peculiar brand of patient care.

"We want to save lives," says Waynick, one of the few who have signed up to be a future head and a trunk in one of the tanks. "And if the result of that is that fewer people will go to funeral homes, I will feel bad for the funeral homes. But I will feel better for the people." sm

Things to do when you’re dead

When Sir James Dewar pioneered cryogenics, inventing the vacuum flask and producing liquid hydrogen in the 1890s, the Scots scientist could never have imagined that his work would have led to cryonics, where corpses are cooled to a state of cryostasis and natural decay is suspended.

In the UK, there is as yet no equivalent to Alcor, the US corpse-storage facility, but last year Britain’s first cryogenic freezer was installed at Plymouth International Business Park and registered as a medical device for the storage of human tissue samples. And though just two Scots, now living in the US, are listed as members of Alcor’s UK branch, the company has had five enquiries from Scotland about their services. Cryonics Europe, meanwhile, is a support and discussion group based in Sussex, with members in Scotland, England and Ireland.

Cryonics is not the only unusual way of dealing with the human body after death. Star Trek creator Gene Roddenberry was blasted into orbit in the world’s first space funeral in 1997. He was joined in the Pegasus rocket (above, with inventor Antonio Elias) by the remains of 1960s drug guru Timothy Leary and rocket scientist Kraffte Ehricke. Houston-based Space Services offers this trip for £530 per gram of cremated remains.

If you’d like a more glitzy final destination, why not have the carbon in your ashes compressed and converted into a Lifegem (left)? These jewels cost from £1,320, rising to £7,395 for a .90 to .99 carat gem. It works for animals, too - the ashes of a pony named Lucky were recently set in a ring for his owner, at a cost of £2,250.

Burial at sea is perhaps a more common request, although there are only 50 British burials at sea a year, and there are only three UK locations where they can take place - to avoid bodies being washed up or trawled back up by fishing boats. American company Eternal Reefs can get around these complications by adding the ashes of your loved one to a commercial reef ball (right) in the Gulf of Mexico.

For an eco-friendly funeral contact the Natural Death Centre, which campaigned in 1991 for cardboard coffins to be made available in the UK. There are now seven varieties to choose from - and more than 180 natural burial grounds, run by local authorities, farmers and charities. Under Scottish law it’s possible to be buried on your own land and you can have your ashes scattered anywhere, including your garden, though some environmental and health checks must be made first. Green party leader Mike Woodin stuck to his ecological principles when he was buried in a cardboard coffin - it was towed to the cemetery by bicycle.

Alternatively, exhibitionists can undergo preservation by plastination, where body tissue is saturated with special plastics, allowing it to be displayed in upright, lifelike poses and enabling the corpse to take part in one of Professor Gunther von Hagen’s controversial Body World exhibitions. And there is an even more eccentric route, followed by undertaker Bill Earl, the author of Your Death is My Life. When Earl died last October, he chose to have his coffin decorated with cauliflowers, in line with his maxim: "The only useful flowers are cauliflowers."

Gaby Soutar