New, easily verifiable criteria for the global exponential stability (GES) and the global practical exponential stability (PGES) of generalized Cohen–Grossberg neural networks with time-varying delays are presented. The analysis leverages a generalized Halanay inequality and the theory of Dini derivatives to establish results that are less restrictive than previous approaches. The derived conditions are validated through three illustrative examples, confirming the theoretical advancements and their practical utility.