In 1977, Schwarzenegger began a relationship with hairdresser Sue Moray after meeting her in Venice, California. "When he was in town, he would be committed to me and I would live with him and go to work from his house. But when he was out of town, we were free to do whatever we wanted and to date anyone else we wanted," Moray said about their relationship in a 2011 interview with The Sunday Times (via Mirror).
For a while, Schwarzenegger allegedly dated Moray and Shriver at the same time but he and Moray eventually called off their relationship once he and Shriver began getting more serious.