Despite the Stray Cats' seemingly instant stardom, record companies are hardly falling all over themselves to sign rockabilly-based bands. The feverish pursuit of cute pop acts in the wake of the Knack's overnight success in 1979 or, more recently, the deluge of synth-pop recordings, are more typical of the record industry's trend-mongering. No one plays follow-the-leader better than large record companies. Yet, their reluctance to jump on a rockabilly bandwagon is probably wise simply because the Stray Cats triumphed despite rockabilly, not because of it.

The only '50s-style rocker who can compete with the Stray Cats' international popularity is Britain's Shakin' Stevens. Much like Cliff Richard, another British superstar sprung whole from Elvis Presley's swiveling hips, Stevens has enjoyed massive hits everywhere but America. His latest release, "Give Me Your Heart Tonight" (Epic BSE38449), is an impressive collection of polished rockers that draw equally on rockabilly and Louisiana rock 'n' roll.

The propulsive "Josephine," replete with Dixieland horns, and the bouncy "Oh Julie" show that Stevens is a talented songwriter, one who can polish a song until it's radio-cized without sacrificing sincerity. More of the success of the album is due, however, to the imaginative wedding of New Orleans horns and Cajun accordions with more straightforward guitar-based rock 'n' roll.

The record's standout is the title tune, "Give Me Your Heart Tonight," a beautiful ballad opened by a dreamy accordion and set to a light rhumba beat. Stevens sings like an understated Presley, using a similarly broad vocal range, but with much less dramatic effect. If Stevens has escaped popularity in America, it's probably because his easygoing adult image and joyful classicism don't strike as deeply with young rock fans as the rebellious narcissism and primitivism more typical of American rockabilly.

Much more indicative of the Stray Cats' impact is the Rockats' six-song mini-LP, "Make That Move" (RCA MFLI 1-8507). This young band, which will perform at the 9:30 club Saturday, predates the Stray Cats but had little real success in earlier, rowdier incarnations. Now they have called in a contemporary producer, Mike Thorne, and, armed with a canyon of echo, a synthesizer and some fat and jazzy guitar chords, they have taken unimaginative aim at the dance club deejays who, after all, got the Cats rolling.

The first side of the record eschews the '50s altogether, offering instead unconvincing hard rock, soul and synth-pop tunes. The flip side is all rockabilly oriented, but Dibbs Preston's drab vocals and the band's needless pursuit of the Stray Cats sound sink even Buzz and the Flyers' excellent "Go Cat Wild."

Rock 'n' roll fans who find all this nouveau rockabilly secondhand or, worse, disingenuous, should flock to the Morells, an American band that serves up good-time rock 'n' roll as unpretentious, tasty and greasy as a roadside hamburger. In fact, one of the best cuts on the album, "Shake and Push" (Borrowed 3302), is "Reds," a light-hearted rockabilly tribute to their favorite burger joint in their home town of Springfield, Mo.

If this band's midwestern distillation of American rock-'n'-roll styles and offhand humor grant the album a casual, garage-band atmosphere, its mastery of these styles and musicianship is thoroughly professional; it's just not out to prove it.

Lead singer Lou Whitney provides a lot of the humor here, moving from a jivey Louis Armstrong imitation on "That Mellow Saxophone" to the sound of a panting degenerate on "You're the One That Done It" and on to the moonshine-addled drawling redneck on "Big Guitar." Throughout, the instrumental hero is D. Clinton Thompson, whose command of jazz, rockabilly and surf styles and repertoire of musty classics would border on the academic if he weren't having so much fun with them. Although the Morells may lack the seriousness and passion of the Blasters, their more lighthearted reclamation of America's past is equally seductive and, honestly, more fun.

Those who believe all real rockabilly ceased to exist after 1959 can take heart in the "reissue consciousness" seizing American record companies.

Of special worth is "For the First Time Anywhere" (MCA-27059), a collection of previously unissued Buddy Holly master tapes, mostly from early 1956. Before Holly had any hits, he recorded a number of songs at Norman Petty's Clovis studio without Petty's production help. While these songs were later released in the "Reminiscing" album, they are presented in all of their unadorned simplicity here. Listening to great thumping rockers like "Rock-a-Bye-Rock" or "I'm Gonna Set My Foot Down," it is clear that this is an outstanding rockabilly band, albeit one still months away from the great the pop band that hit with "That'll Be the Day."