Branigan toured Europe as a backup singer with Leonard Cohen. She started her solo career in 1982. Her first album, "Branigan", was released in 1982. A song "Gloria" from that album stayed on top of the pop charts for 36 weeks. It reached number six on the British pop charts. It was a remake of an Italian song from the 1970s. The song got her a nomination for a Grammy for best female pop singer. She was nominated for three more during her career. She released seven more albums. She co-wrote the song "How Am I Supposed To Live Without You?" with a then unknown Michael Bolton. In 1981 Branigan appeared on German television in "An American Girl in Berlin". She was a guest on the American TV show, "CHiPS". She starred in the movie "Mugsy's Girls" in 1984. She also appeared in the 1988 movie "Backstage". In 2002 she starred in the Off-Broadway production of "Love, Janis", playing Janis Joplin. She received rave (very good) reviews for her performance.