Apple’s cool quotient is part of the problem: when the company introduced its iTunes download service in Europe in mid-2004, customers snapped up 800,000 songs in the first week. Apple now owns 70 percent of the local entertainment-download market, and ivory iPod earbuds are as ubiquitous in Soho as they are in, well, Soho.

That’s the problem, say a growing number of European consumer advocates. They’re taking aim at the digital-rights-management (DRM) software in iTunes, included at the behest of record labels to stop piracy. The way Apple (and for that matter, Microsoft) implements DRM prevents songs bought on iTunes from being played on non-Apple gadgets like cell phones. It also blocks songs downloaded from other sites, like Yahoo or Napster, from being transferred to iPods. “It is an abuse of the power that Apple has in the market,” says Ewald van Kouwen, a spokesman for the Netherlands’ Consumer Association. “iTunes is a great store, but iPod and iTunes should not be combined.”

That’s the same argument European regulators used against Microsoft back in 2004, when they forced the software giant to unbundle its Media Player from Windows. As early as last summer, Norway’s consumer-protection agency filed a complaint claiming that iTunes violated Norwegian law by tying consumers’ hands. By the year-end, regulators in Finland, France, Sweden, Denmark and Germany had also opened investigations into whether the software was unfair. On Jan. 27, the Dutch upped the ante by setting a September deadline for Apple to dump DRM, a month earlier than a similar deadline laid down by Norway. “The way Apple uses DRM is illegal,” says Norway’s consumer ombudsman Bjoern Erik Thon. Still, Apple won’t face any real consequences unless the Norwegians go a step further and take the matter to court, in which case the company could be fined for noncompliance.

Indeed, there are few legal parallels between the Microsoft and Apple cases. But both reflect Europe’s deep anxiety about its lack of clout in the digital world. Aside from Skype (now owned by eBay), it’s tough to think of a truly disruptive digital company that’s emerged from Europe. Instead the French and German governments have poured millions of euros of taxpayer money into a Google copycat called Quaero, a project that embarrasses some European techies, who’d rather see more support for entrepreneurs. On Feb. 13 a Belgian court levied a $33,000-per-day fine against Google for displaying copyrighted materials in its search results. “I think this case is all about European politics,” says Mark Mulligan of Jupiter/Kagan Research in London. With $9.6 billion in revenue from digital entertainment in 2006, Apple may simply be too fat a target to ignore. “It’s the curse of success,” says Keith Woolcock, a technology analyst with Westhall Capital in London.

Apple has mounted a savvy defense. Earlier this month CEO Steve Jobs released an open letter distancing his company from the reviled DRM software. He points out that he can only ensure copyright protection—demanded by the major music labels, three of which are European—if the Apple system is closed off. One alternative, he wrote in his letter, would be “to abolish DRMs entirely … DRMs haven’t worked, and may never work, to halt music piracy.” (Apple declined to comment beyond Jobs’s letter.) Indeed, London-based EMI is already experimenting with DRM-free down-loads of songs from artists including Norah Jones and Lilly Allen.

And the wrangles have yet to hit Jobs where it really hurts. Apple’s European sales were up 33 percent last year, to $4.1 billion. The region accounts for a quarter of the company’s total revenue. The most likely outcome is that the labels will admit DRM isn’t solving their piracy problems, as Jobs suggests, and together they and Apple will stumble toward some sort of open system. That would be music to Apple’s ears.