Despite efforts by several European designers to capture the American sportswear business, it's hard to beat Ralph Lauren and Calvin Klein at their own game.

Taking over center court at the Seventh Regiment Armory Monday night, Lauren used a runway far longer than the tennis court there to serve up a strong and steady sportswear collection for next fall.

A rumor that Nancy Reagan would be showing up at today's Calvin Klein presentation encouraged many of the editors, particularly the group from London, to arrive at Klein's showroom off Seventh Avenue more than half an hour before his scheduled show. The rumor proved false, but those who did show weren't disappointed. Last year, Klein abandoned his signature casual sportswear for fitted, sophisticated clothes. For next fall he has gone back to the familiar sportswear classics that he once made known worldwide as a strictly American style.

Lauren included men in his show for the first time in years. The opening sequence of men, women and children strolling happily down the runway in nifty handknit sweaters and tweed pants looked like a page from one of the Lauren catalogues that help generate his $1 billion a year in sales.

The changes in the Lauren collection are subtle but not unfamiliar. His handknit sweaters, with skiers knit into some of the designs, are reminiscent of Sun Valley in its best days; some sweaters and jackets borrow collars, buttons and shaping from Tyrolean classics; blazers, in navy with burgundy piping, are revived as sweaters; coat dresses are now double-breasted and collarless in cashmere as coats or dresses. Lauren pairs an English riding jacket with skinny pants cut like ski pants in stretch fabric with a stirrup under the foot.

Lauren likes skirts below the calf when they are pleated and full, but cut off just at the knee for narrow styles. But most of all he likes classic, pleated-front pants worn with jackets, cashmere sweaters or coats.

In menswear, tweedy suits are sometimes not perfectly matched. There are more double-breasted styles than usual; vests are double-breasted, as are several of the jackets and tuxedos.

"People already have enough clothes," said Lauren before the show. "But I'm in business. I've got to give people some reason for buying. I guess I'm giving them a quality of clothes that hasn't been around in a long while."

Lauren is a big believer in people wearing his clothes for years. He said it strongest when he showed up in old jeans and a denim shirt to take his bow at the end of the show.

"It is not easy deciding what to wear for your own show," Calvin Klein said with a laugh a few days before his opening. He was thinking of wearing a black-and-white sports jacket. "That's the way I feel about clothes these days. But people may think I'm just trying to copy my own collection."

Klein carved his renewed classic shapes sharply in black and white. The boxy coats, in which he excels, were shown off well in black-and-white plaid or check, usually teamed with pin-striped or windowpane-plaid trousers and a cashmere turtleneck sweater or silk blouse in a strong color. Although black and gray come through strongly, he's not afraid of a strong color palette for such familiar classic shapes as pea jackets, long skinny sweaters and tunics in jersey or satin. But when it comes to evening, black velvet, black lace and black satin are the ways Klein thinks one can stand out in a crowd.

Klein doesn't know why fitted clothes were right for last year, but not this year. He tosses aside the suggestion other designers have made that fitted clothes never sold well and adds, "Well, mine did. But I just feel it is the moment for easy, square, boxy clothes." Many of his sweaters and jersey dresses left the option open for those women who still like fitted clothes. And the sequined and beaded velvet dresses in his finale were simpler versions of his styles last year as well.

For himself, he finally decided to wear his new black-and-white sports jacket when he took his bow. He wore it over a Fruit of the Loom T-shirt and jeans. His pal, Bianca Jagger, who was first in line to congratulate him, was wearing one of Klein's black-and-white plaid jackets from the show. "I guess you know how I feel about the collection," she said with a grin.