Among prominent features of the visual networks, movement detections are carried out in the visual cortex. The visual cortex for the movement detection, consist of two layered networks, called the primary visual cortex (V1), followed by the middle temporal area (MT), in which nonlinear functions will play important roles in the visual systems. In this paper, the fundamental characteristics in V1 and MT model networks, are discussed by analyzing the asymmetric neural networks. V1 and MT model networks, which are decomposed into nonlinear sub-asymmetrical networks. By the optimization of the asymmetric networks, movement detection equations are derived. Then, it was clarified that the even-odd nonlinearity combined asymmetric networks, are fundamental in the movement detection. These facts are applied to two layered V1 and MT networks, in which it was clarified that the second layer MT has an efficient ability to detect the movement.