Electronic Journal of Differential Equations, Vol. 2005(2005), No. 73, pp. 1-17. Title: Existence results for a second-order abstract Cauchy problem with nonlocal conditions Authors: Eduardo Hernandez M. (Univ. de Sao Paulo, Brazil) Mauricio L. Pelicer (Univ. de Sao Paulo, Brazil) Abstract: In this paper we study the existence of mild and classical solutions for a second-order abstract Cauchy problem with nonlocal conditions. Submitted January 25, 2005. Published July 5, 2005. Math Subject Classifications: 47D09, 47N20, 34G10. Key Words: Abstract Cauchy problem; Cosine functions of operators