Summary: A generalized Halanay inequality is established, and the boundedness of generalized Cohen-Grossberg neural networks [

*M. A. Cohen* and

*S. Grossberg*, IEEE Trans. Syst. Man Cybern. 13, 815–826 (1983;

Zbl 0553.92009)] is investigated. By applying the generalized Halanay inequality and Lyapunov functional methods, new sufficient conditions are obtained ensuring the global exponential stability of solutions of generalized Cohen-Grossberg neural networks with variable delay. Three examples are also given for illustration.