In this paper, a sufficient condition for existence of an overshoot in the step response of fractional-order systems is presented. Based on this condition, it can be shown that the existence of an overshoot in the step responses of some classes of fractional-order systems (for example, the class of fractional-order systems having commensurate orders between 1 and 2) is unavoidable. To show the usefulness of the obtained condition, this condition is applied to prove some results on the time response analysis of fractional-order control systems. (C) 2011 Elsevier Ltd. All rights reserved.