The main problem with "The Marrying Man" is a simple one: It's a comedy and it isn't funny.

The leads are appealing - Kim Basinger as a torch singer who seems to be patterned after Madonna doing Marilyn, and especially Alec Baldwin in a Cary Grantish playboy role.The story is interesting - supposedly based on a real-life situation where a volatile couple married and broke up and married again three or four times.

And the supporting cast features some enjoyable character players - Robert Loggia, Paul Reiser, Elisabeth Shue, Armand Assante.

Yet the script, by Neil Simon of all people, doesn't develop the characters or even define them very well, lets the story meander all over the place and has very few laughs. It doesn't help that first-time live-action director Jerry Rees (he also helmed the animated feature "The Brave Little Toaster") lets the film, though slick, hang together rag-ged-ly.

"The Marrying Man" is set primarily in the late '40s and early '50s. Baldwin is a Los Angeles millionaire who has never worked a day in his life. He is heir to a toothpaste fortune and about to marry the daughter (Shue) of a powerful Hollywood producer (Loggia).

Six days before his wedding, he goes to then-budding Las Vegas for a bachelor party with four buddies (Reiser, who narrates the film; Fisher Stevens, Steve Hytner, Peter Dobson). At a casino they watch the floor show and see a young singer (Ba-singer), and it's lust at first sight for Baldwin.

Though he's told she is the girl-friend of gangster Bugsy Siegel (Ar-mand Assante), Baldwin just can't resist making a pass, and later in the night Bugsy catches them in the act.

Instead of killing Baldwin and Ba-singer, however, he forces them to get married. Naturally, neither of them wants marriage - or so they think - so they have it annulled and go their separate ways.

Fate, with a nudge from Simon, has other plans, of course, so they eventually are thrown back together - several times.

All of this has the makings of very funny stuff on the order of an old Ernst Lubistch screwball comedy, especially when Baldwin has to take over the family business in Boston and Basinger has to learn to cope with the chic elite.

But whether it was tension on the set (Premiere magazine recently did an article on Basinger's and Bald-win's alleged temper tantrums, which supposedly caused major setbacks in production) or just a dull script by Simon, the possibilities are never realized.

Even the supporting characters, usually a strength in a Simon film, seem to be just hanging around with little or no purpose.

"The Marrying Man," rated PG-13 for sex, violence, profanity and vulgarity, is simply not funny.

And as a postscript, yes, according to the movie's press kit, Basinger really did sing all her own songs - complete with the silly cartoon sexuality she displays, which may remind viewers of Madonna's antics on the Oscar show.