Mammalian motor control is implemented by a combination of different networks and system, working coherently to plan the movement of the body or a limb and to execute this movement a dynamical environment. While it is believed that complex, voluntary movements are planned in the motor areas of the cortex, the execution of the movement is controlled by a combination of cortical and cerebellar networks together with central pattern generators and reflex circuits in the spinal cord. In this thesis, we propose an abstract model that captures the basic properties of mammalian motor control, using the example of two different movements: arm movements as well as locomotion. Our model consists of three parts: first a high-level network, that learns movements, using a combination of actor-critic based reinforcement learning and Optimal Control theory. The second part corresponds to spinal reflex circuits that execute basic movements of the musculo-skeletal system. They are modeled by a simple neural network, that learns the dynamic properties of the muscoloskeletal system by the mechanism of spontaneous motor activity (muscle twithing) combined with a Hebbian learning rule. We demonstrate that this network can learn the antagonistic control of joint movements. The final part of the model is a cerebellar network, that translates a complex movement trajectory, such as reaching, and activates the spinal reflex circuits to execute the movement. The mapping between the cerebellar neurons and the spinal reflex circuits are trained with artificial neural networks. Using a musculoskeletal arm model, we demonstrate that the proposed neural motor control model can generate the movement to arbitrary goal position.