Symmetries are often helpful in reducing the complexity of the analysis of dynamical systems. Here we discuss a symmetry that combines a transformation in space with a scaling of time Examples are given. of a number of nonsmooth dynamical systems in which a symmetry of this type occurs. The time-scaling symmetry can be combined with return mapping analysis to achieve a dimension reduction in addition to the one already obtained from considering the return map. The method is applied in a study of Zeno behavior in linear systems with relay feedback. (C) 2009 Elsevier Ltd. All rights reserved.