(FORTUNE Magazine) – The Recording Industry Association of America may have won a legal victory against Napster, but now it's scrambling to keep up with the next generation of music-swapping software. The conventional wisdom said that these under-the-radar services would never pose the threat that Napster did because they are such a pain to use. Anyone who still believes that hasn't tried to download a new Janet Jackson track lately: Many of the bugs have been worked out, and user numbers are soaring. Stopping the services will be "a long process," concedes Cary Sherman, general counsel for the RIAA. FORTUNE recently asked top execs at six of the most popular ones, where you can still find a broad selection of free copyrighted music, why they'll have more staying power than the old Napster did.

Hit Me, Baby, One More Time

[Aimster]

The RIAA recently sued Aimster, run by CEO Johnny Deep from his upstate New York home. His defense: Aimster is mainly a messaging service like the U.S. mail. "Nobody's saying, 'Check that package. Maybe there's a bootleg CD in there.'"

[BearShare]

BearShare creator Vincent Falco, CTO of West Palm Beach company Free Peers, says BearShare should be safe from the RIAA because it connects users to a decentralized file-swapping network called Gnutella rather than to a centralized one like Napster.

[IMesh]

IMesh is based in Israel, so there's probably no way the RIAA can touch it. Still, CEO Elan Oren says he's trying to comply with an RIAA request to remove 500,000 copyrighted tunes. Alas, he laments, "it's going to take ten years or something to find all those songs."

[KaZaA]

Niklas Zennstrom, CEO of Dutch company FastTrack (owner of KaZaA), insists he is negotiating with the Dutch music industry to offer copyrighted songs legitimately. Meanwhile, he says, "if they were to try and put us out of business, that would be a dictatorship."

[MusicCity.com]

Mike Weiss, CEO of Nashville-based MusicCity (which distributes file-sharing software called Morpheus), maintains that the law is on his side: "If it is judged that file-sharing technologies are illegal, then you might as well shut down the entire Internet."

[WinMX]

Says Kevin Hearn, president of Frontcode Technologies in Windsor, Ontario (which launched WinMX): "I don't believe our good Members of Parliament have enough disrespect for our constitutional rights to pass a Canadian equivalent of the Digital Millennium Copyright Act."