In the last few decades it has been proven, that the cerebellum takes part in learning the bulk of motor control. The mechanisms which provide such properties are still largely unknown, but an involvement of parallel fibers and climbing fibers in this process, as have been proposed decades ago in cerebellar learning theories, is now clear. Among difficulties of the learning theories is an evident necessity for spontaneous activity of the cerebellar climbing fibers . Recently, the group of M. Mauk proposed an elegant explanation of this inconsistency [11, 12]. We present here a stochastic model of a cerebellar module, based on this new approach. Theoretical treatment yields some consequences for experimental verification. Besides an explanation of real cerebellar functions, the analyzed control system presents a new paradigm for neural network memorizing systems.