Eye blinking classical conditioning is one of the most extensively studied paradigms related to the cerebellum. In this work we have defined a realistic cerebellar model through the use of artificial spiking neural networks, testing it in computational simulations reproducing the eye blinking classical conditioning in multiple sessions of acquisition and extinction. We used two models: one with only the cortical plasticity and another with three plasticity sites, one plasticity at cortical level and two at nuclear level. We have compared the behavioral outcome of the two different models and proved that the model with a distributed plasticity produces a faster and more stable acquisition of conditioned responses in the reacquisition phase with respect to the single plasticity model. This behavior is explained by the effect of the nuclear plasticities, which have a slow dynamics and can express memory consolidation and savings.