Sarah Jessica Parker, 36, and Matthew Broderick, 40, are expecting their first child, a representative of the actress confirmed to PEOPLE on Friday. The baby is due this fall, said the rep. Parker plays sex columnist Carrie Bradshaw on HBO’s “Sex and the City” (HBO, like PEOPLE, is part of AOL Time Warner), and Broderick recently concluded a year’s run as the timid accountant Leo Bloom in the Broadway smash “The Producers.” He soon will begin shooting an ABC TV movie adaptation of the stage musical “The Music Man.” Parker’s pregnancy has caused HBO to shut down production of “Sex and the City” this week and delay the series’ fifth-season premiere at least until July. (It was originally slated for June.) Her pregnancy will figure into the story line, however — the question being, who is the father, says NBC News. Before marrying Broderick in 1997, Parker dated John Kennedy Jr. and Robert Downey Jr. And before he married Parker, Broderick dated actress Lili Taylor and had been engaged to Helen Hunt and Jennifer Grey. Over the past few months rumors have circulated that the Parker-Broderick marriage was in trouble. The stories were further fueled when Parker neglected to mention her husband (who was nowhere in sight) in her acceptance speech at January’s Golden Globes ceremony, where she was named Best Actress in a comedy series for “Sex.” At an amfAR benefit in February, Broderick’s then-Broadway costar, Nathan Lane, 45, joked onstage with Broderick, citing the Golden Globes snub and asking aloud in front of the crowd: “Is your marriage all a show-biz scam put together by your Scientologist managers?” Replied a deadpan Broderick: “It was a very big misunderstanding. If you were to watch the tape very closely, indeed, she did thank me. In Morse Code.” Broderick said she was blinking her gratitude with her eyes.