The new field of learning control devleops controllers that learn to improve their performance at executing a given task, based on experience performing this task. the simplest forms of learning control are based on the same concepts as integral control, but operating in the domain of the repetitions of the task. This paper studies the use of such controllers ina decentralized system, such as a robot with the controller for each link acting independently. The basic result of the paper is to show that stability of the learning controllers for all subsystems when the coupling between subsystems is turned off, assures stability of the decentralized learning in the coupled system, provided that the sample time in the digital learning controller is sufficiently short.