"Run Baby Run" was the fourth part of the suite included on the Sweet Revenge album, telling a story about a girl being tempted by a Devil. It was released as the second single from Sweet Revenge. The B-side, depending on territory, was either "Follow Me", or its reprise version or "The Stud", all from Sweet Revenge. The song was a typical Lear-Monn collaboration, with Amanda Lear providing the lyrics and Anthony Monn composing the music and producing the track. Arrangement is credited to the Germany-based producers, Charly Ricanek and Rainer Pietsch.

The song did not chart, but remains one of Lear's most recognizable and popular tunes to date.

A music video was produced as a part of Italian TV show Stryx. It pictures Lear dancing in a leopard-dotted dress among other Stryx cast members rolling on the floor. It was directed by Enzo Trapani.

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