Ladies’ man Arnold Schwarzenegger has finally admitted to having what he refers to in his new memoir as a “hot affair” with Brigitte Nielson while they were filming the movie “Red Sonja” in 1985.

Nielson gave some details of the romance–which Schwarzenegger claims was just a “fling”–in her own memoir last year, and now he’s confirming it. The affair occurred while he was living with Maria Shriver, and the action star/former governor insists that the tryst with Nielson only made him realize that he wanted to marry Shriver.

The news comes on the heels of the revelation of his affair with housekeeper Mildrid Baena, which produced a son. While many people probably assumed there was something going on between Schwarzenegger and Nielson, it’s somewhat surprising to some that Schwarzenegger would come clean now, after all these years, especially after news of his indiscretion with Baena caused a rift between him and Shriver; the couple are now estranged and living apart.

“I think it was the stupidest thing I’ve done in the whole relationship,” Schwarzenegger said in an interview with 60 Minutes last night. “It was terrible. I inflicted tremendous pain on Maria and unbelievable pain on the kids.”

The new book, due out next week, also talks about Shriver’s attempts to talk her husband out of running for office in California and the subsequent talk she had with her mother, Eunice Kennedy, about the women in their family supporting their husbands in every endeavor.