Based on several new Lyapunov–Krasovskii functionals, by employing the homeomorphism mapping principle, the Halanay inequality, a nonlinear measure approach and linear matrix inequality (LMI) techniques, several delay-independent sufficient criteria are obtained for the existence, uniqueness and globally exponential stability of considered neural networks. Without assuming the boundedness and monotonicity of activation functions, the obtained conditions generalize some previous results in the literature. Two examples are also given to show the less conservativeness of the obtained conditions.