PARIS — When Bertelsmann, the German media giant, boasted of a financial resurgence last week, one of the strongest growth stories came from one of its most traditional businesses: the book publisher Random House.

Random House said sales of digital books had more than tripled last year, lifting overall revenue 6 percent. E-books, Random House said, accounted for 10 percent of U.S. sales.

So much for the good news. Outside the United States, however, the digital book business is still in its infancy.

During a news conference in Berlin, Markus Dohle, chief executive of Random House, predicted that Europe would catch up with the United States in two to five years.

For that to happen, some big problems will have to be solved. Too few e-reading devices have found their way into European consumers’ hands, and too few titles are available to them in digital form.

While booksellers like FNAC in France and Thalia in Germany have introduced e-book readers, the Amazon Kindle is conspicuously absent from much of Europe. The company has introduced an international version of the device, but outside Britain, where Amazon recently opened a Kindle Store, there are virtually no local-language books available for European Kindle users.

Some European publishers have balked at licensing their works for digital sale via Amazon, fearing cannibalization of physical sales, as well as the U.S. giant’s reputation for hardball negotiations over pricing.

Other devices that allow book reading, like the Apple iPad, are more widely distributed in Europe. But few European publishers have licensed their works for sale on Apple’s digital store.

Meanwhile, European legislative and regulatory developments are further clouding the picture.

Last week, the French Senate approved a measure under which publishers could set the retail price of e-books, so that a title would cost the same whether it was sold by, say, Apple or a French-owned e-book store. The proposal would extend into the digital realm a pricing system that governs the sale of ink-on-paper books in France and several other European countries, preventing booksellers from offering discounts.

Publishers say single-price rules support independent booksellers and encourage them to stock a diverse range of titles, rather than filling their shelves with cut-price bestsellers. These systems have deep cultural roots, and regulators have generally tolerated them, despite frowning on price-fixing in other forms.

But there are signs that the European Commission is going to be stricter about the pricing of digital books. Last month, commission officials raided the offices of a number of European publishers, saying they had “reason to believe that the companies concerned may have violated E.U. antitrust rules.”

Publishing executives say the regulators are scrutinizing the so-called agency model of pricing, under which publishers set the retail prices of e-books, with the online retailers taking a commission.

Amazon prefers to buy books from publishers on a wholesale basis and then set its own retail prices. But it reluctantly adopted the agency model in the United States recently.

If European regulators do not like the agency model, it is hard to imagine that they could live with the proposed French law. In addition to allowing publishers to set retail prices, it would apply to any digital retailer operating in France, even Web sites based elsewhere in Europe. That, according to some publishing executives, sounds like a violation of E.U. e-commerce rules, which are intended to encourage cross-border business.

Working out these seeming contradictions could take years. In the meantime, the European e-book market may continue to lag behind.

If European books remain unavailable via legitimate digital outlets, the threat of piracy will grow. Publishers, politicians and regulators need only look at the music industry to see what that means.

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