Asymmetrical neural networks are shown in the biological neural network as the catfish retina. Several mechanisms have been proposed for the detection of motion in biological system. Hassenstein and Reichardt network(1956) and Barlow and Levick network(1965) of movements are similar to the asymmetrical network developed here. To make clear the digerence among these asymmetrical networks, we applied non-linear analysis developed by N. Wiener. Then, we can derive u-equation of movement, which shows the direction of movement. During the movement, we also can derive the movement equation, which implies that the movement holds regardless of the parameter a. By analy2ing the biological asymmetric neural networks, it is shown that the asymmetric networks are excellent in the ability of spatial information processing o n the retinal level. Then, the symmetric network was discussed by applying the non-linear analysis. I n the symmetric neural network, it was suggested that memo~ function is needed to perceive the movement.