In this paper, the existence of oscillations for a class of recurrent neural networks with time delays between neural interconnections is investigated. By using the fixed point theory and Liapunov functional, we prove that a recurrent neural network might have a unique equilibrium point which is unstable. This particular type of instability, combined with the boundedness of the solutions of the system, will force the network to generate a permanent oscillation. Some necessary and sufficient conditions for these oscillations are obtained. Simple and practical criteria for fixing the range of parameters in this network are also derived. Typical simulation examples are presented.