It's a picture of eternal damnation. Twenty-four hours a day, in a sterile laboratory outside Nuremberg, training shoes are enduring purgatory; purgatory on a grand, Hieronymous-Bosch scale. Rows of metal hooks swing back and forth, picking at the trainers' tongue leather. Aluminium weights press down on their soles with industrial monotony, while a woman annotates their viscosity and elasticity. From a computer terminal she instructs a steel arm to scrape them across asphalt, astroturf and linoleum - all in the name of calculating their friction coefficient. Some style experts may say that trainers are dead, but from the look of this adidas laboratory, they will be dragged around the nine circles of Hell first.

Trainers still constitute 40% of total shoe sales in the United States, and Nike are the largest shoe manufacturer in the world. But analysts are talking about market saturation. Americans just decided that they owned more than enough pairs of Nikes, and Nike's very success started counting against it. What cool kid wanted a new pair of Nikes if they were what his Dad was wearing? Or, even worse, his grandma? When Nike's profits and share prices tumbled in the spring, headlines declared that the $8 billion (£5 billion) wholesale domestic American sports-shoe market was witnessing a glut of product, and a uniformity of marketing strategy.

One of the things helping adidas right now is that it's not Nike. Unsurprisingly, adidas insist that reports of the death of the trainer have been greatly exaggerated. They know that spoils in the trainer war are still considerable. They also know that the downturn has happened before. Three years ago, everybody got into Timberland boots. The trade called it 'the brown shoe phenomenon' - a sudden fashion switch away from trainers to variations on work boots by brands like Rockport and Caterpillar. It's a recognised cycle in the footwear market that just happened to coincide with the start of Nike's downturn. Adidas just plans to keep investing in training-shoe research.

Catherina McKiernan, winner of the 1998 London Marathon, is running - repeatedly - across the adidas laboratory floor. A woman in a white coat films her feet, at 500 frames per second. The frames are then frozen to show the distribution of McKiernan's body weight. Her heel is vertical (unlike a lot of runners, whose heel hits the road at an angle), but stability isn't a problem. McKiernan runs on the forefoot of her trainer. Adidas designers assemble and confer. No, she doesn't need extra shock absorption on her heel for the Amsterdam marathon. McKiernan will run in your basic road shoes. But even they are the result of God-knows-how-many years of biomechanic theory.

Over the years, trainer designers have brought us Hydroflow, Gel, ARC, Torsion, ERS, Twist, Pump, Disc, React and Huarache. Whether we wanted them or not. The best known technological breakthrough is Air - that little cushioning bubble Nike put in the heel of their shoes. It's not actually air (it would seep out) but a concoction of inert "fat" gases. Not that the technology actually makes a great deal of difference - all consumers really care about is whether the trainers are available in red. Adidas estimate that youths wear 80 per cent of their product for leisure, and 20 per cent for sport. The majority of buyers want trainers for nothing more strenuous than a walk to the pub.

Trainers began life back in the 1830s, when Dunlop developed 'sand shoes' as beachwear for the Victorian middle classes. They became known as plimsolls because the line where the rubber and canvas bonded looked similar to the Plimsoll line around a ship's hull. Business was low key until Fred Perry wore Dunlop Green Flash to win Wimbledon three times running. It was the earliest example of sports-star endorsement. Marketing sorts saw what the publicity did for sales. It wasn't until the 1970s that America's jogging and aerobics booms really kick-started trainer sales to the general public. Then came hip-hop and the real growth in trainers as street wear.

Trainers somehow glued together the 20th-century obsessions of sport, fashion and technology. And whether it's the thickness of the sole, or the position of a stripe, the trainers you wear speak volumes about you and your place in the lexicon of cool. It's no accident that sportswear companies want to endorse stars such as John McEnroe and Diego Maradona - stars who somehow seem to have achieved personal fulfilment through winning and self-expression. Andre Agassi, Mike Tyson and Eric Cantona are today's anti-heroes, connecting that Nineties mind-and-body thing with rebellious, degenerate individualism. Trainers link kids with this new outlaw world.

"But it's changing" says Mikal Peveto (35), adidas' senior product manager (footwear) and a trainer geek. "The formula used in basketball - have a great basketball player, name a shoe after the great basketball player, sell a lot of shoes - it doesn't work any more. There's one guy who set a standard - Michael Jordan - but he's out on his own. [Jordan actually wanted to wear adidas in the first place, but they couldn't match Nike's sponsorship offer]. It's an anomaly. Don't factor it into your equation, because when he's gone, that formula's gone. Things are blurring now. Endorsements are complicated. To some people, it's just as meaningful to see Liam Gallagher wearing Gazelles as it is David Beckham."

Football has always been adidas' game. But, in order to achieve the goal of chairman Phil Knight (a turnover of $12 billion by 2002), Nike has been forced to compete. In the 1994 World Cup, held in the USA, Nike didn't sponsor one national team - in France it had six, including Brazil. Adidas sponsored France, the eventual winners, but had less luck with it's individual players. "We don't regard David Beckham as the five weeks of the World Cup" says Peter Csanadi, head of adidas' global public relations. The 38-year-old started with adidas Hungary, but the only relic is his taste in knitwear. "We regard David Beckham as the season before with Manchester United, the qualifying rounds, and then next season. And Zidane [who was sent off] the same way. For us the World Cup is just a signpost - not a destination."

Adi Dassler began making sports shoes in Germany in 1920. It did his reputation no harm when Jesse Owens wore a pair of his spikes to win four Olympic gold medals in 1936. He formed the adidas company in 1948, with the three stripes as his logo. Blue Ribbon Sports (the name Nike - the Greek goddess of victory - came to one the partners in a dream) was founded 25 years later, in Portland, Oregon. Nike grew from humble beginnings. A local graphic designer was paid only $35 for the Nike "swoosh". Nike eventually superseded adidas, and became the world's biggest sportswear company, with an annual turnover of $9 billion - 35 per cent of the global sportswear market.

But over the years Adidas has created a fair share of its own problems. In the 1980s, American suppliers became unreliable. And the company wasn't listening to the marketplace. The classic example was adidas' refusal to add more cushioning to its running shoes for the Americans, who ran on concrete roads and not the cinder trails of Europe. And there was no investment in technology. "Take a look at the sl72 and the sl76" says Peveto. "It's the same shoe, with a slight toecap. And those shoes were four years apart. We were in 26 of the 28 olympic sports, but our entire catalogue was only two mm thick. Now we're designing more, but we missed 1985-1995. That was a tough decade to miss in a business like this.

"When Horst Dassler (Adi's son) died, adidas wasn't a family business anymore" says Peveto. "The money makers took over. But you get to a point where you're so far behind that you're ahead. We were so out that we were in." Adidas recognised there was money to be made by remaking the shoes we loved as children. Replicas of the company's famous early trainers - the Gazelle, the Super Star and the Oberliga - picked up on trainer nostalgia, and enhanced the desirability of the originals. And how. The antique dealers' bible of prices, Miller's Collectables, recently advertised a pair of adidas trainers (c. 1971, worn, US size 9) for £300-£350.

Adidas is still function based. Even the branding is function - the three adidas stripes were originally mid-foot arch bandages, designed to give extra support. "It's a mistake to try and sell adidas as a fashion brand" says Csanadi. "We would be subject to the volatile trends of the fashion market. In 1994 we could have sold six or seven times as many Gazelles as we actually did. But we said 'This is the allocation for a country - we don't want to sell more'. We only made them available in selected outlets. We had to avoid being interpreted as a fashion brand. Sport drives the street - the street does not drive sport. So all this street credibility - we don't call it fashion - comes from core, authentic sports values."

Technology will shape the future of sports footwear. Especially the materials for growth areas such as 'individualistic' sports like snowboarding and skateboarding and 'outdoor adventure' like scrambling and canyoning. One sportswear company is rumoured to be developing trainers with microchip sensors which change the shoe's molecular structure when necessary. Before long, all the companies will offer custom-made trainers. If the Gap and Levi Strauss can do it with their made-to-measure jeans, then why not adidas? It's already in the mind of every sport's company product manager. Technically it isn't a problem, but it is likely to prove expensive.

Technology or no, adidas still employ a coolhunter. It's up to Lisa Broomhead, the youth communications manager (even though she's 31), to predict trends. "Adidas is in fashion" she says. "It's not a fashion brand, but it's in fashion. And you can't ignore that". Broomhead, who previously worked on textiles development at Nike, has to reckon what will be 'culturally significant' two years in advance. She shows adidas designers round Cool Britannia to get inspired - from Clerkenwell, to Camden market, the Ministry of Sound and Soho. "Hopefully I can pre-empt what people will want in the future. Because the UK is such a small country, fashion changes very quickly. What's in one day can be out the next. I try and tell adidas what's happening - art, technology, cars, Sony Playstations or films. We have to be way ahead."

The 'coolhunting' idea makes the team back in Germany laugh. Out loud. "These designers go to London and go to clubs because that's who they are. They wanna go to the clubs. They go to Paris or the Louvre because they wanna get out of Herzogenaurach [the village where Adi first made his trainers]. You don't need to go to a club in New York to know a goodlooking shoe from an ugly shoe. It makes me laugh when I hear the guys are going to the Ministry of Sound for inspiration. They go just because they want to go - and write off a trip. I can hear them saying 'This design was inspired by a reptile from my trip to Guatemala'. Just be honest - you wanted to go to Guatemala."

But fashion will make or break adidas. That's why the company is learning to be more reactive. In 1986, Run DMC were the first rap group to crossover to music's mainstream. And one of their biggest successes was the rhyme My Adidas. The rappers even wore the adidas A-15 tracksuit. But it took a year for adidas to bring out Run DMC hi-tops. If there is a flaw in adidas corporate culture, it's a lack of communication. "That's probably where DKNY, Ralph Lauren and Tommy Hilfiger [who are all getting in on the trainers market] see the big, giant opportunity" says Peveto. "The fashion thing. When you get down to it, we're just a bunch of broken down jocks who make running shoes. But we do really love our business."

You still won't see adidas platform trainers. "Buffalo-inspired stuff?" says Peveto. "They're so absolutely bad for you. But now I pick up a catalogue and see Fila are doing them. I say 'You're going to die Fila. It's no wonder you're dying'. Get off your turf, chase that fashion stuff, and you're going to get slaughtered. I like it when they're on our turf. We still have Catherina McKiernan and Haile Gerbsaillasie, the hard-core long distance runners. And when Tommy Hilfiger goes out and tries to endorse a basketball player, he's got decades, decades and decades to go to catch up with the credibility of the real sports brands. Ultimately, cream rises and shit sinks."