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We study the existence of mild solution of a class of nonlinear nonautonomous fractional integrodifferential equations with nonlocal conditions in a separable Banach space . Combining the techniques of operator semigroup, noncompactness measures, and the fixed point theory, we obtain new existence of mild solution without the assumptions that the nonlinearity satisfies a Lipschitz type condition and the semigroup generated by is compact. An application of the abstract result is also given.