Electronic Journal of Differential Equations, Vol. 2002(2002), No. 07, pp. 1-14. Title: Nonlocal quasilinear damped differential inclusions Authors: Mouffak Benchohra (Univ. de Sidi Bel Abbes, Algerie) Efrosini P. Gatsori (Univ. of Ioannina, Greece) Sotiris K. Ntouyas (Univ. of Ioannina, Greece) Abstract: In this paper we investigate the existence of mild solutions to second order initial value problems for a class of damped differential inclusions with nonlocal conditions. By using suitable fixed point theorems, we study the case when the multivalued map has convex and nonconvex values. Submitted December 18, 2001. Published January 15, 2002. Math Subject Classifications: 34A60, 34G20, 35R10, 47D03. Key Words: Initial value problems; multivalued map; damped equations; mild solution; evolution inclusion; nonlocal condition; fixed point.