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Impulsive differential equations arise naturally from a wide variety of applications such as aircraft control, inspection process in operations research, drug administration, and threshold theory in biology. There has been a significant development in the theory of impulsive differential equations in the past 10 years, especially in the area where impulses are fixed. However, the corresponding theory of impulsive delay differential equations has been less developed due to numerous theoretical and technical di culties. Recently, the existence and uniqueness of results for impulsive delay differential equations for which impulses occur at fixed times have been presented in [1]. In this paper, we shall extend these results to impulsive delay differential equations for which impulses are state-dependent. Moreover, by adapting the techniques used in [3] for impulsive differential equations without delay, we then establish …