The authors study the global existence of a solution to nonlinear evolution equations with nonlocal conditions of the form
in a real Banach space . Here, is a nonlinear -accretive (possibly multivalued) operator on , and . Using the Schauder fixed point theorem, the Fryszkowski selection theorem and some properties of compact semigroups, the authors prove the existence of integral solutions. This work is a continuation of the paper by S. Aizicovici and Y. Gao [J. Appl. Math. Stochastic Anal. 10, No. 2, 145-156 (1997; Zbl 0883.34065)].