Summary: The problem of stability of the equilibrium of a class of neural networks with transmission delays is studied using the Lyapunov functional method and combining with the method of inequality analysis. Some sufficient conditions for global asymptotic stability of neural networks with transmission delays, which do not require symmetry of the connection matrix and nonlinear properties for neural units to be continuously differentiable or strictly monotonic increasing, are obtained. These conditions can be used to design globally stable networks and thus have important significance in both theory and applications. In addition, we give some examples to illustrate the main results.