Nonlinear Sobolev-type integrodifferential control systems defined in Banach spaces are considered. Several assumptions concerning both the linear and nonlinear parts of the abstract state equations are listed. Using compact semigroup theory and Schauder's fixed point theorem, sufficient conditions for exact controllability in a given time interval are formulated and proved. As a simple illustrative example, exact controllability of a semilinear distributed parameter system is studied in detail. Moreover, several remarks and comments on approximate and exact controllability problems for semilinear abstract control systems are presented. Similar controllability problems for nonlinear integrodifferential control systems have been recently considered in the paper [\textit{K. Balachandran}, \textit{P. Balasubramanian} and \textit{J. P. Dauer}, J. Optimization Theory Appl. 84, No. 1, 83-91 (1995; Zbl 0821.93010)].