Abstract: In this paper we discuss the existence results of the integral solutions to nonlinear evolution inclusion:u'(t)∈Au(t)+F(t,u(t)), where A is m-dissipative and F is a set valued map in separable Banach spaces, and extend the relative results in references.

Key words: nonlinear evolution inclusion, m-dissipative operator.equicontinuous semigroup, integral solution, Hausdorff measure, Kamke function