They've got it. That swish comic style of 1930s plays and films, which has come back into vogue to be mangled painfully on the modern stage and screen, has been captured in "Death on the Nile," a full-star cast production of the 1938 Agatha Christie mystery.

It's strange about fashions in decades. Right now, the entertainment world is working on both the '30s and the '50s, while the clothing industry has the '40s. A bit of the '40s has crept into the look of this film, and inevitably a tiny bit of '70s sound, but both are minimal. What was achieved was the luxury of detail and timing that made up the dramatic style of that time.

Agatha Christie deserves it. We are used to accepting popular entertainment that offers plot - the chase-thriller - or character - portraits of introspective neurotics - but seldom both. Christie does offer both. She may have used them more than once, but the plot structure of several isolated people all with grudges against the same obviously doomed person, and the character of Hercule Poirot, the Belgian dectective who has to keep correcting people who think he is French, are durable enough.

And they are worth clothing richly, in the best of actors, locations, photography and dialogue. The film was made in Egypt, the wonders of which are splendidly used, as when the victim and all potential murderers are sightseeing at the Temple of Karnak and shown framed at different angles, between columns and among colonnades, with no sound but the dicking of reverent tourist feet. John Guillermin was the director, and Jack Cardiff the director of photography.

The story concerns a rich young woman, whose responsibilities include the tedium of having to sign her name to renew the lease on the Chrysler Building, who steals her friend's beau and takes him off to Egypt for a honeymoon, on which they are quickly joined by two detectives, her New York lawyer, the jilted friend and assorted other eccentrics, many of them with their own retainers, each of whom, down to the maids and paid companions, has been supplied with his or her own little tributary of a motive, feeding into the plot's main stream, which is also the River Nile.

It's a joy, after having so many modern film thrillers spoiled by the indistinguish-ability of the characters, rather like a Miss America Pageant where you have trouble recognizing the contestant you've decided to root for, to have each suspect fully done as a character. This is done, not only with broad satiric strokes, but with a wealth of telling little mannerisms.

Peter Ustinov's Poirot sleeps in a hairnet and just manages to keep down his amazement at his own cleverness, as if it were a rising burp that politeness forbids letting out. When he pointedly inquires whether someone he is questioning is able to face eating his lunch, the great detective reveals with tremendous condescension his true purpose, which is to eat it himself.

Angela Lansbury, as the author of such passionate novels as "Snow on the Sphinx's Face," has a divinely lolling look for expressing her great appetite, whether for a fussy old gentleman or a golden little drink. Bette Davis and Maggie Smith play twowell-born ladies, Davis now still rich but greedy and Smith now her impoverished companion, who keep the bounce going between "amiable eccentricity and downright rudeness" like a good Ping-Pong game. Jack Warden spews contempt and probably saliva as a German psychotherapist whose indignation at being a suspect is expressed in such lines as "What would I have to do with the sordid affairs of the lower classes? It is well known that they do not have the neurosis - only the animal passions."

Throwaway lines and phrases abound in this theatrical style, where you throw out a pearl and then walk past it. In fact, the heroine's pearl necklace is referred to - only once, and that quickly in passing - as "the Potsdam Pearls." David Niven, as the detective's dumb companion, the one who helps the audience by needing to have every thing explained to him, starts when Poirot mentions his hunger, "J'ai faim." "You have a woman?" asks the startled but impressed second banana who thought he'd said "femme."

And the human detail - the revolutionary who looks just slightly queasy at the sight of blood, the Indian ship manager who shouts "Goody goody gumdrop!" when the murder weapon is found - is such that the merely adequate performances of the romantic trio, by Mia Farrow, Lois Chiles and Simon MacCorkindale, fit in well as sort of background stability.

DEATH ON THE NILE: K-B Cinemo, K-B Cinema 7, K-B MacArthur and Springfield Mall.