This article deals with the controllability of nonlinear differential systems which arise when a linear system is perturbed. The sufficiency conditions presented insure that the nonlinear system will be (globally) controllable whenever its linear part is controllable. Moreover, the steering can be accomplished using continuous controls with arbitrarily prescribed initial and final values.The problem of splitting the nonlinear system into controllable and uncontrollable parts is also discussed along with the nature of the null domain of controllability.