Electronic Journal of Differential Equations, Vol. 2009(2009), No. 22, pp. 1-10. Title: Existence of solutions for differential inclusions on closed moving constraints in Banach spaces Author: Adel Mahmoud Gomaa (Helwan Univ., Cairo, Egypt) Abstract: In this paper, we prove the existence of solutions to a multivalued differential equation with moving constraints. We use a weak compactness type condition expressed in terms of a strong measure of noncompactness. Submitted December 1, 2008. Published January 27, 2009. Math Subject Classifications: 32F27, 32C35, 35N15. Key Words: Differential inclusions; moving constraints; existence solutions.