Electronic Journal of Differential Equations, Vol. 2002(2002), No. 47, pp. 1-9. Title: Nonlocal Cauchy problems for first-order multivalued differential equations Author: Abdelkader Boucherif (King Fahd Univ. of Petroleum and Minerals, Saudi Arabia) Abstract: We prove the existence of solutions for a nonlocal Cauchy problem for a first-order multivalued differential equation. Our approach is based on the topological transversality theory for set-valued maps. Submitted January 27, 2002. Published May 28, 2002. Math Subject Classifications: 34A60, 34G20. Key Words: Cauchy problems; multivalued differential equations; nonlocal condition; topological transversality theorem.