The Ocean's Twelve star has a boy and a girl in Los Angeles

Julia Roberts has given birth to twins – a boy and a girl – in a Los Angeles hospital, PEOPLE has learned. Their names are Phinnaeus Walter Moder and Hazel Patricia Moder.

The 37-year-old actress, who is married to cameraman Danny Moder, 35, gave birth at about 3 a.m. Sunday morning, a source tells PEOPLE. Mother and babies are doing fine. No other details are available.

Late last month, Roberts was admitted to an L.A. hospital after experiencing a series of early contractions. The condition was not serious, and the contractions eventually stopped, but doctors advised bed rest until she gave birth.

Roberts and Moder have kept a low profile since marrying on July 4, 2002, at her 82-acre ranch in Taos, N.Mex. The decidedly private couple split time between their homes in Taos, Venice, Calif., and New York City.

Twins, it turns out, run in Roberts’ family: Her great grandmother and a pair of cousins are twins.

Roberts has two movies opening next month: Ocean s Twelve, with George Clooney and Brad Pitt, and Closer, an adult drama directed by Mike Nichols.