The cerebellum plays a major role in motor control. It is thought to mediate the acquisition of forward and inverse internal models of the bodyenvironment interaction [1]. In this study, the main processing components of the cerebellar microcomplex are modelled as a network of spiking neural populations. The model cerebellar circuit is shown to be suitable for learning both forward and inverse models. A new coupling scheme is put forth to optimise online adaptation and support offline learning. The proposed model is validated on two procedural tasks and the simulation results are consistent with data from human experiments on adaptive motor control and sleep-dependent consolidation [2, 3]. This work corroborates the hypothesis that both forward and inverse internal models can be learnt and stored by the same cerebellar circuit, and that their coupling favours online and offline learning of procedural memories.