(FORTUNE Magazine) – Back in the late 1980s, when Margaret Thatcher was in her prime, the perfect present for an upwardly mobile Brit was an Amstrad. A what? That was the clunky, whirring desktop computer produced by Alan Sugar, a brash London entrepreneur who decided to take on IBM and Apple. Sadly, like the Apricot, the Tulip, and dozens of other European computer names you've never heard of, the Amstrad logged off in the mid-1990s, beaten into submission by Dell, Compaq, and the rest of the industry's heavy brigade.

Now, after a quiet decade, a few European PC makers, like France's Cibox, think they are strong enough in their own backyard to compete with American giants like Dell and Compaq. And two of them, Germany's Maxdata and Britain's Tiny, are taking aim at the U.S. market. Do they have a prayer?

Not if the past is prologue. In the 1980s and '90s, Europe's problem was that, while the region had (and has) some great engineers, its first generation of PC manufacturers never figured out how to become genuine mass producers--the kind of operations that count their output of vanilla boxes in millions rather than tens of thousands. Unlike American titans such as Dell, Compaq, and Hewlett-Packard, which were building critical mass in the world's largest PC market, European companies were too focused on their national markets to bother playing the volume game.

That didn't matter so much in the 1980s, when PCs were as strange to most Europeans as televisions had been to their parents. But it started to matter in the 1990s, when the multinationals--Japanese as well as American--hit Europe in force and began to sell PCs as commodities. Computer prices tumbled and profit margins were shaved thinner than silicon wafers. The Europeans sank. Even a large and storied European company like Olivetti drifted out of the computer business in the late 1990s, having failed to establish a transnational brand. "In the last two years, the medium-sized European computer companies have really taken a pasting," observes Howard Seabrook, who directs research into Europe's PC market for Dataquest in Britain.

But don't write off the old world's PC industry just yet. After a decade of decline, Europe's computer sector is experiencing a modest renaissance. Seabrook reckons that up to 500 European companies make more than 1,000 PCs a year, and at the top end of the ladder, a handful boast a significant national market presence.

The stakes are huge. The European PC market hit 30 million units last year and is expanding at an annual rate of more than 20%. There's plenty of potential for growth. In Germany, 45% of adults have access to a PC at home, but fewer than 40% do in Britain, and barely 30% in Italy and France.

Europe's niche players are betting that there will be enough room for everybody to play the computer game. Take Cibox, the French PC brand launched in 1997 by Yaacov Gorsd, an ebullient 28-year-old entrepreneur of Russian-Tunisian parentage. Last year, Cibox came from nowhere to sell 150,000 PCs and claim 4% of the French market, with turnover of $123 million. "The only difference between us and the big American companies," Gorsd declares with Gallic bravado, "is the financing to realize our ambitions."

Or consider Viglen, a British PC manufacturer with sales of around $160 million in 1999. On Jan. 18, Viglen's price on the London stock market more than doubled when news leaked that it was planning to launch an Internet investment fund. Principal beneficiary of that vote of confidence? Alan Sugar. Yes, Britain's most famous PC salesman is back. Sugar took over Viglen in 1994, spun it out of his Amstrad consumer electronics group in 1997, and then bought 73% of the stock under a share-repurchasing plan last year.

But here's a simple message for any European PC manufacturer who imagines that the home side, having learned from past mistakes, just might topple the multinationals' regional dominance: Sober up. In the first nine months of 1999, most PC sales in western Europe (the EU plus Norway and Switzerland) were scooped by a familiar roll call: Dell, Compaq, Hewlett-Packard, Fujitsu-Siemens, Packard Bell-NEC, and, in the notebook sector, Toshiba.

True, Germany's Siemens makes the list and has a genuine global presence, but only because of the fifty-fifty joint venture it forged last October with Fujitsu. Minus the Japanese, Siemens would simply be the leading player in Germany, and a bit player everywhere else.

Undaunted by the overwhelming odds, Europe's PC makers believe they have a key advantage: local knowledge. "Look," says Cibox's Gorsd, pointing to his own product: "Open this up, and what's the difference between my machine and anyone else's?" Not much, he continues, but his advantage is that he understands how to sell the product in France and, in particular, how to deal with hypermarket chains like Auchan and Carrefour, which sell around 80% of all consumer PCs.

In Britain, Viglen earns around a third of its income selling PCs to the country's schools and universities. That doesn't seem sexy business, until you take on board the Labour government's commitment to spend up to $2 billion over the next few years to wire up education. Says Bordan Tkachuk, Viglen's CEO: "The watchword for a company like us is get niche or get out."

Staying a small (or at most a medium-sized) company producing several hundred thousand PCs annually might not seem an inspiring destiny. But a decade after the Amstrads and the Olivettis had their moment of glory, it could be Europe's best bet for keeping a foothold in the PC market.

Two European companies, however, have much grander ambitions. Britain's Tiny and Germany's Maxdata believe they can become global contenders. Their chosen field of combat: America. If you're an optimist, it's called taking the battle deep into enemy territory. But if you're skeptical about the chances of any heavyweight PC maker's emerging from Europe, tilting at America looks like folly.

Maxdata thinks it can prove the skeptics wrong. Founded in 1987, this German manufacturer expects to report 1999 pretax profits of more than $100 million, on turnover of $1.1 billion. Maxdata is big (or biggish) in Germany, where it sold around 600,000 units in 1999, for a 6% market share. It also sold another 150,000 PCs in other European countries, suggesting that it has gone further than most in breaking out of its national box. But a German invasion of America? Why not? asks Joachim Gut, Maxdata's executive in charge of production. "Europe is one of the toughest markets in the world, so if you can compete with the big multinationals here, there's no reason why you can't do the same in the U.S." According to Gut, Maxdata's lethal weapon is speed, with a build-to-order model in Europe that can deliver PCs to customers within three to four days of purchase. In America, where the company will adopt a direct Internet sales model when it opens for business later this year, Maxdata aims to be just as fast. It will need to be, since Dell, Gateway, and the rest of the competition are not exactly slowpokes.

Meanwhile, American PC shoppers can already check out a British manufacturer, Tiny, that in the past two years has been thinking very big indeed. Since the start of 1999, Tiny has opened 25 showrooms in California, Oregon, and Washington State, and by the end of 2000 the company plans to launch a further 75 branded retail outlets on both the West and East coasts. Neil Stevens, Tiny's 31-year-old product and marketing director, argues, "In many ways the U.S. is very similar to the U.K.," citing the two countries' shared language, as well as Britain's receptiveness to American direct-sales methods. He adds: "A lot of computer brands in the U.S. have been successful in the U.K., but no one has ever done it the other way." He doesn't see why the traffic shouldn't go in both directions.

For all its heady ambitions, Tiny remains a corporate enigma. Registered offshore on the island of Jersey, a U.K. tax haven, the privately held company refuses to disclose the names of its main shareholders. Tiny is based in Redhill, Surrey, a nondescript commuter town just south of London, but don't expect a tour of its boxy headquarters to disclose much about the way the company operates, other than its passionate dislike of overhead. There's a cramped call center, a warehouse at the back, and a set of Spartan executive offices upstairs. Stevens estimates that in the fiscal year ended January 2000, revenues will have doubled to $800 million. Worldwide unit sales of PCs should reach 360,000. About 80% of all Tiny's sales are in the U.K., where it has a 6% market share, behind Dell (17%), Compaq (16%), and Packard Bell-NEC (8%) but ahead of Toshiba, IBM, and Hewlett-Packard. Tiny's problem: "There's only so much more market we're going to take in the U.K.," because the retail environment is so harsh, says Stevens. He adds that while profits are "strong," margins are constantly being "squeezed" by the competition.

So it's off to America. To see how seriously Tiny takes the U.S., click onto its American Website (www.tiny.com). There, the surfing eyeballs can learn that Tiny is "the PC company that outsells Gateway in the U.K. nearly two to one." It's almost impossible to check that claim, because Gateway won't break out its British numbers, but Mike Swalwell, who heads Gateway's regional operation, offers Tiny some advice about punching above its weight. Says Swalwell (who is British, incidentally): "Gateway isn't going to be the only problem for Tiny in America. They're up against some really big guys."

Stevens is convinced that Tiny can succeed in the U.S. "We're like McDonald's," he explains: "Wherever you go in the world, the concept's the same and the product's the same." Well, yes--but that's also true of Dell, Gateway, and others. Tiny perhaps goes further than these multinationals in sticking to a limited range of about 20 PCs, aimed particularly at first-time buyers. "We're trying to take the fear out of buying a computer," Stevens says. Once an order is placed, Tiny guarantees that the product will reach the customer within a week. Says Stevens: "We are very, very fast, because we are not trying to be all things to all people."

If the speed theme sounds familiar, it's because Michael Dell was singing the same tune almost a decade ago. But in America, even more than Europe, size counts these days, because relentlessly falling PC prices have put a premium on economies of scale. And in the size stakes, Tiny is a pipsqueak compared with America's homegrown giants. Research by International Data Corp. shows that in the last quarter of 1999, when U.S. sales slowed, Dell still shifted 2.1 million units, followed by Compaq (two million), Hewlett-Packard (1.3 million), and Gateway (1.2 million). Tiny's U.S. sales for the whole year: around 30,000.

Tiny and Maxdata might defy the odds and become serious contenders in America. "In this industry, anything can happen," says Dell's head of European operations, John Legere, citing his own company's meteoric rise. But ask Legere whether European companies represent a serious threat, and the most he'll say is that they're "interesting to watch"--and he's talking about Europe, not America. That gives you some idea of the distance the region's more ambitious PC producers must travel before the computer giants quake in their boots.