New neural network approach to the control of arbitrary nonlinear plant is presented. The approach is based on the model of cerebro-cerebellar interaction during the learning of new visuo-motor transformation. The model in turn is based on four main prerequisites: the Marr-Albus-Ito theory of cerebellar learning, the equilibrium point theory of motor control, the columnar organization of the cerebral cortex and the differential neurocontroller theory. The convergence of the learning procedure is proved for the linear plant. Its convergence for nonlinear plants are confirmed by computer simulation of arm reaching movements in the horizontal plane.