Nonlinear nonautonomous control systems describable by ordinary vector differential equations are considered. Approximate and exact methods for decomposition into serial or parallel connections of subsystems of lower order are presented. It is assumed that the treated control systems are globally or locally decomposable. Certain controllability properties of the systems given in decomposed form are studied. Several special cases are considered and sufficient conditions for complete controllability in fixed time interval and local controllability along the trajectory are presented and proved. Local path controllability is also considered and some results are given. Similar decomposition problems for nonlinear control systems have been treated by the first author [SIAM J. Control Optimization 20, 311-327 (1982; Zbl 0485.49025) and J. Math. Anal. Appl. 91, 305-318 (1983; Zbl 0529.93010)].