Learning control refers to controllers that learn to improve their performance at executing a given task, based on experience performing this specific task. In a previous work, the authors presented a theory of indirect decentralized learning control based on use of indirect adaptive control concepts employing simultaneous identification and control. This paper extends these results to apply to the indirect repetitive control problem in which a periodic (i.e., repetitive) command is given to a control system. Decentralized indirect repetitive control algorithms are presented that have guaranteed convergence to zero tracking error under very general conditions. The original motivation of the repetitive control and learning control fields was learning in robots doing repetitive tasks such as on an assembly line. This paper starts with decentralized discrete time systems, and progresses to the robot application, modeling the robot as a time varying linear system in the neighborhood of the desired trajectory. Decentralized repetitive control is natural for this application because the feedback control for link rotations is normally implemented in a decentralized manner, treating each link as if it is independent of the other links.