The matter of finding the relevant conditions for the existences of the integralmanifolds to evolution equations is a great interest of many Mathematic researchers.The first studies on the existence of integral manifolds on differential equations incase finite-dimensional phase spaces were given by Hadamard [5], Perron [12], andBogoliubov and Mitropolsky [1, 2]. Next, Daleckii and Krein [3] extended theseresults to the case of bounded coefficients acting on Banach spaces. Later, Henry[10], Sell and You [13] proved the case of unbounded coefficients, and the papers byN.T.Huy [6,7] in which nonlinear part satisfies the -Lipschitz condition. However,the existences of the integral manifolds near periodic solution of evolution equationswith Nemytskii’s nonlinear operator have been studied in no researches before.Therefore, in this paper, we would like to prove the existence of local stablemanifolds near periodic solutions to evolution equationse form u A t u g u t ( ) ( )( ) where the operator-valued function t A t ( ) is T -periodic, and the Nemytskii'soperator g x t ( )( ) is T -periodic with respect to t for each fixed x and satisfieslocally Lipschitz condition.