Summary: By using generalized Halanay inequality and \(M\)-matrix, both the global exponential stability and periodic oscillatory solutions are discussed for a class of reaction-diffusion generalized neural networks with time-varying delays. Several new sufficient conditions are obtained to ensure existence, uniqueness of the equilibrium point, and its global exponential stability of the equilibrium point and the existence of periodic oscillatory solutions of reaction-diffusion generalized neural networks with time-varying delays. The results extend and improve the earlier publications. In addition, this condition requires neither the activation functions to be differentiable, bounded, and the weight-connected matrices to be symmetric, nor time-varying delays and generalized terms to be differentiable. Moreover, an example is given to show the effectiveness of the obtained results.