The paper considers the restrictions which must be placed on the poles and zeros of a system function of a linear system with lumped constants in order that the response of the system to a step-function drive should be monotonic. Necessary and sufficient restrictions are derived for a system function (driving-function/response-function) containing up to three zeros, and these are interpreted as permissible pole-zero positions on the complex plane for the one- and two-zero cases and also for a number of instances in the three-zero case.The paper concludes with a method of obtaining sufficient conditions for monotonic response in the case of more complicated system functions from the results given in the paper.