Cage married Ms Kim two months after divorcing Lisa Marie Presley

Former waitress Ms Kim, who married the Face/Off and Adaptation star in July 2004, gave birth to son Kal-el in New York on Monday.

Kal-el is the birth name given to comic book hero Superman, who Cage was once linked with playing on screen.

Annett Wolf, publicist for Cage, said: "They are healthy and happy and it's quite lovely."

Cage, who won a best actor Oscar in 1996 for his role in Leaving Las Vegas, has another son with actress Kristina Fulton.

His two previous marriages, to actress Patricia Arquette and singer Lisa Marie Presley, ended in divorce.