Fractional nonlinear nonautonomous dynamical control systems are considered. The notion of controllability is introduced and discussed. Using the methods of fractional calculus, it is shown that controllability in a given time interval is strongly connected with the two-point boundary problems for fractional control systems. Moreover, sufficient conditions for controllability of nonlinear fractional control systems are formulated and proved using the linearization method. It is shown that a nonlinear fractional control system is controllable when its fractional linear part is controllable. Several remarks and comments on controllability problems for fractional linear and nonlinear dynamical control systems are also given. Similar controllability problems for fractional control systems have been recently considered in the paper [A. B. Shamardan and M. R. A. Moubarak, Controllability and observability for fractional control systems, J. Fractional Calc. 15, 25-34 (1999; Zbl 0964.93013)].