Nonlinearity is an important factor in the biological neural networks. The motion perception and learning in them have been studied on the simplest type of nonlinearity, multiplication. In this paper, asymmetrical neural networks with nonlinear function, are studied in the biological neural networks. Then, the nonlinear higher-order system is discussed in the neural networks. The second-order system in the nonlinear biological system is shown to play an important role in the movement detection. From the theoretical analysis, it is shown that the third-order one does not contribute to the detection and the fourth-order one becomes to the second-order in the movement detection function. 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 difference among these asymmetrical networks, we derive α-equation of movement, which shows the detection of movement. During the movement, we also can derive the movement equation, which implies the movement direction regardless of the parameter α.