In this paper we study a class of neural networks with continuously distributed delays. By means the of yapunov functional method, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution. We also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified. Therefore, our results play an important role in the design of globally exponentially stable neural circuits and periodic oscillatory neural circuits.