In this seminar, we present sufficient conditions for the convergence of asymptotic systems in non-autonomous Cohen-Grossberg neural network models that incorporate both infinite discrete time-varying and distributed delays. The main stability criterion is obtained by imposing conditions under which the non-delay terms asymptotically dominate the delay terms. As an application, we provide sufficient conditions ensuring that all solutions of a non-periodic neural network model with unbounded delays converge to a periodic function as time goes to infinity. A numerical example is presented to illustrate the effectiveness of the new results. This is a joint work with A. Elmwafy (PhD student) and César M. Silva of University of Beira Interior, Portugal.