The rate equation for an arbitrary mth-order growth or decay reaction can be expressed in terms of the q-exponential function exp(q) f = [1 + (1-q) f](1/(1-q)), with q equal to m. The analysis suggests that a wide variety of reaction rate (kinetic) processes and models, in chemistry, biology/ecology, unit operations and contaminant transport, are amenable to analysis by Tsallis' non-extensive statistical mechanics. A number of q-analogues of common kinetic mathematical models are proposed, and illustrated by several examples. Crown Copyright (c) 2005 Published by Elsevier Ltd. All rights reserved.