Fame has its benefits, but it counts for little at the marriage bureau in downtown Manhattan. Which is why heads turned April 15 when a statuesque and very pregnant Uma Thurman and boyfriend Ethan Hawke patiently waited their turn for a $30 state marriage license with other sweethearts in the Municipal Building. At the New York City April 20 film premiere of Les Misérables, Thurman, who turns 28 on April 29 and is due in July, shrugged off questions about just when she might saunter down the aisle. But the license is good only for 60 days, and friends say a wedding is almost as imminent as it is eagerly anticipated by the groom-to-be. "Every time he mentioned Uma's name," says Salma Hayek, who filmed Velocity of Gary with Hawke, 27, last fall, "you could see drool come out of his mouth."

Hawke began salivating when he and Thurman, who was married briefly to actor Gary Oldman in the early 1990s, met while making the sci-fi thriller Gattaca in 1996. The pair kept their romance low profile (even refusing to enter the film's premiere together) until last year, when they began to be spotted sharing quiet dinners at restaurants in Manhattan. More recently they purchased a house north of New York City in a town where neighbors include Al Pacino and Bill Murray. In February the couple discussed the merits of cloth versus disposable diapers in a baby shop in Vancouver, where Hawke, there to shoot Snow Falling on Cedars, practiced his diapering skills on a life-size doll.

"There was lots of cuddling and affectionate play between the two of them," says store clerk Avrell Smith. "They seemed very much in love." Devotion is a given, but at least one question remains unresolved: what to call their bundle of joy. "With Uma," Hawke joked early this year, "it'll be a really strange name."