Employing Brouwer’s xed point theorem, matrix theory, a continuation theorem of the coincidence degree and inequality analysis, the authors make a further investigation of a class of cellular neural networks with delays (DCNNs) in this Letter. A family of sufcient conditions are given for checking global exponential stability and the existence of periodic solutions of DCNNs. These results have important leading significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs. Our results extend and improve some earlier publications.