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This paper studies stability problems of a class of impulsive systems with time delay whose linear parts contain unstable system matrices. By using the method of variation of parameters, Lyapunov functions and inequalities, several stability criteria are established for both linear and nonlinear impulsive systems with time delay. It is shown that the time delay systems can be stabilized by impulses even if the system matrices are unstable. Several numerical examples are given to illustrate the results.