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This paper focuses on the problem of delay- dependent stability analysis of neural networks with variable delay. Two types of variable delay are considered: one is differentiable and has bounded derivative; the other one is continuous and may vary very fast. By introducing a new type of Lyapunov-Krasovskii functional, new delay-dependent sufficient conditions for exponential stability of delayed neural networks are derived in terms of linear matrix inequalities. We also obtain delay-independent stability criteria. These criteria can be tested numerically and very efficiently using interior point algorithms. Two examples are presented which show our results are less conservative than the existing stability criteria.