We　study　an　initial-boundary　value　problem　for　a　nonlinear　evolution　system　with　damping　and　diffusion;　our　main　purpose　is　to　investigate　the　boundary　layer　effects　when　the　vanishing　diffusion　limit　alpha　-＞　0(+),　especially　for　the　mixed　boundary　conditions;　we　prove　that　the　thickness　of　layer　is　of　the　order　O(alpha).　Furthermore,　the　corresponding　convergence　rates　are　also　obtained.