While they sue over first album, their second drops off pop chart.

Few acts in pop-music history have struck as much terror in the hearts of parents as the Beastie Boys.

The rap trio's 1986 debut album, ''Licensed to Ill,'' was a window-rattling mix of heavy-metal guitars and sexy party rhymes. In support of this controversial masterwork, the group launched a debauched concert tour featuring caged dancers and provocative sexual prop.

The bawdy antics were undercut by a dopiness many fans found endearing. The Beasties extolled the joys of hedonism with such bumbling abandon that critics and fans hailed them as a harmless, madcap parody of wasted youth.

But the Washington, D.C.-based Parents Music Resource Center (PMRC) was buying none of it. The pop-music watchdog organization headed by Tipper Gore (wife of Tennessee Sen. Albert Gore) cited ''Licensed to Ill'' on a list of offensive pop albums. The hysteria spread to the heartland, and some people in the nation's capital even sought to ban the group from performing.

''We learned how to tick people off,'' said Adam ''MCA'' Yauch, reminiscing about those halcyon days.

But that was a couple of years ago, a long time in the world of rock 'n' roll. Now the airplane wreck pictured on the group's debut album, once a symbol of the Beasties' hard-partying lifestyle, could be viewed as an illustration of the group's flagging fortunes.

The group's Capitol Records album ''Paul's Boutique,'' which was released last July, has sold a mere 500,000 copies - a fraction of its multimillion-selling predecessor. (The album this week dropped off Billboard magazine's pop chart).

Meanwhile, royalties from the Beastie Boys' best-selling debut album are tied up, pending the outcome of a lawsuit the group filed against its old record company, Def Jam. Def Jam has countered with a suit of its own.

As if the group didn't have enough problems, the K mart department store chain refused to stock ''Paul's Boutique'' due to its potentially offensive lyrics.

''A lot of towns in America don't have any other stores than a K mart,'' Yauch said. ''So some towns can't even buy our album.''

The group has hung tough in the face of outrageous misfortune, and Yauch, Adam ''King Ad-Rock'' Horovitz, and Michael ''Mike D.'' Diamond have vowed to stay together.

Yauch, Horovitz and Diamond may or may not be intimidating separately, but together they can be as terrifying as a sandbox full of unattended tots. The three share a wealth of inside jokes, and it's hard to tell when they are joking or being earnest.

The group claimed to have reduced a reporter to tears recently with its us-against-them tactics.

''She was probably instructed to come back with a bunch of regular answers,'' Diamond explained. ''It's like she was dealing with a format, so the answers had to be really predictable.

''When she didn't get that, she just freaked. A lot of people think you're being disrespectful when you don't give them straight answers. But we just like to be different.''

The determination to be different may have cost them their core audience. On ''Paul's Boutique'' the Beasties have abandoned the rap-heavy metal synthesis that made them popular in favor of a funkier approach. Yauch explained the album was a collaboration between the group and the Dust Brothers, a production crew that includes Tone-Loc producer Matt Dike.

No rules

''We set down a rule that there would be no rules,'' Yauch said. ''The album was the result of that philosophy.''

The Beasties promised to stick to that philosophy when recording a compilation album featuring various acts they discovered recently.

''It's the logical extension for us to do a compilation album like this, because we've always included our favorite five minutes of a certain song and put it all together into one song,'' Diamond said.

At first, the group was not as forthcoming about the lawsuit against its old record company, Def Jam, and the label's chief executives, Russell Simmons and Rick Rubin.

''We're not allowed to talk about Russell's bald head or Rick's fat stomach,'' Yauch said, ''and we can't spend any of the money we made from the first album.''

As the conversation progressed, the band reflected on the lawsuit and its implications.

''We can't buy houses like Rick and Russell with money from the first album,'' Diamond said. ''It's like starting from scratch now. This is like the first album we're going to get paid for.''

Horovitz claimed the group didn't devote much thought to the lawsuits, except during interviews. Should the courts find in favor of Def Jam, the Beastie Boys could lose millions of dollars.

''Imagine how bitter we'd be if we sat around and thought about that all day,'' Yauch said. ''We can spend a bit of time being glad we got out from under that whole incestuous relationship.''

Diamond and Yauch formed the Beastie Boys in 1981 as a hard-core punk outfit. A 7-inch EP, ''Polly Wog Stew,'' failed to catch on with the public.

With the recruitment of Horovitz, the group's luck began to change. In mid-1983, the threesome recorded a tune called ''Cookie Puss,'' which was taken from a prank phone call the group made to an ice-cream company. The single was an underground hit.

Part of the B side of the single, ''Beastie Revolution,'' found its way into the soundtrack of a British Airways commercial without the group's consent. The Beasties later won a ,000 settlement.

Signing with Def Jam in 1984, the group recorded other obscure hits like ''Rock Hard'' and ''Hold It Now Hit It.'' As the opening act on Madonna's 1985 tour, the group was struck by a revelation.

''We learned how to come out on stage and perform in a huge venue of people who wanted absolutely nothing to do with us,'' Horovitz said. ''We were performing before a bunch of people who are just wishing we would leave, but we got a response.''

The band's debut album was released around Christmas of 1986, incurring the wrath of the PMRC and parents nationwide.

''Everybody's got to do something, and those PMRC people are probably just bored,'' Horovitz said. ''They've got nothing to do with their lives, so they harass somebody. We're just making some music from some people who like it.''

Diamond put the PMRC flap into perspective using rap-music parlance:

''Just because Tipper can't rock the mike, doesn't mean she has to be a jealous MC.''