This chapter is devoted to basic properties of nonautonomous generalized ordinary differential equations (ODEs) and to applying some of the results to measure functional differential equations (FDEs) and functional dynamic equations on time scales. It deals with local existence and uniqueness of solutions of generalized ODEs, and provides analogous results to measure FDEs and functional dynamic equations on time scales. It includes results on the local existence and uniqueness of solutions of measure FDEs and functional dynamic equations on time scales. The chapter presents the analogues for measure differential equations and dynamic equations on time scales. It provides the results concerning the prolongation of solutions of generalized ODEs for Banach space-valued functions. These results are fundamental in the study of asymptotic properties of solutions of generalized ODEs.