Nancy Reagan has tapped the best American designers on both coasts to create the costumes she will wear to her husband's inauguration, the inaugural balls and the gala.

The choice of James Galanos, America's foremost designer of elegant clothes, to make the inaugural ball gown is also a sentimental one. Galanos made the gown she wore to the ball after her husband's first inauguration as governor of California -- a white embroidered wool gown that bared the right shoulder.

The new gown, which bares the left shoulder, is a white satin sheath with an elaborately hand-beaded lace overlay. The scalloped hem of the dress develops into a short train. Galanos has made a white satin coat with stand-up ruffle, framing the face. Her white pumps by David Evins and bag by Judith Leiber incorporate the fern design of the gown's embroidery.

For the swearing-in ceremony and the parade on Tuesday, Mrs. Reagan will wear a red dress and coat by designer Adolfo. The outfit features vertical tucking on the torso, and will be worn with a draped, close-fitting hat. Mrs. Reagan's penchant for red has encouraged many to call the bright red color of the outfit "Reagan red."

The black gown with fitted velvet top and satin skirt Mrs. Reagan will wear to the inaugural gala at the Capitol Centre is by Bill Blass. The black fox-edged shrug to be worn with this gown and the mink coat Nancy Reagan has worn here last week have prompted a spokesman for the People for the Ethical Treatment of Animals to ask for an interview with Mrs. Reagan to discuss "the example the First Lady is setting by wearing furs."

Mrs. Reagan, who first started wearing Galanos designs more than 20 years ago, also chose him to design her ball gown for the second California inauguration. In recent years she has passed up his new designs, because his price tags climb to more than $10,000 for hand-embroidered evening gowns. But she has continued to wear the Galanos styles she has bought over the years.

Mrs. Reagan called Galanos, admired by both European and American couturiers for his innovative, contemporary styling and craftsmanship, right after Election Day.

He prepared one design, which she accepted immediately, and he delivered the dress and coat before she left California.

"I know her preference, her special liking for one shoulder and halter styles, and they become her," said Galanos from his studio in Los Angeles. "I wanted Nancy to really look glamorous. She's representing the highest office in the country, in the world. . . I just wanted her to look elegant and in keeping with the new formality."