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This paper investigates the step responses of fractional order systems in the viewpoint of extrema existence in such responses. It is proven that a fractional order system with a commensurate order between zero and one has an extrema-free step response if its integer counterpart has such a step response. In addition, it is shown that the step response of a stable fractional order system with a commensurate order between one and two cannot be monotonic. Based on these achievements, some further results on the step response of different classes of fractional order systems are presented.