Abstract: Even type Lyapunov functions were constructed based on M-matrix theory to study the globally asymptotic stability of Hopfield networks with reaction-diffusion. These networks are generalized without assuming the boundedness, monotonicity and differenciability of the activate functions. The conditions were obtained for globally asymptotic stability of the generalized Hopfield networks, where the interconnection matrices are symmetric or non-asymmetric and the neural activate functions are non-monotonic.