Multiple steady states are often observed in isothermal continuous flow stirred tank reactors (CFSTRs) involving heterogeneous catalysis. At least, when certain physical conditions prevail, even fragmentary multiple steady-state data can be used to help determine the operative catalytic mechanism. This article describes theory that can ascertain both whether a given candidate mechanism has the capacity to support multiple steady states and, more importantly, whether the mechanism has the capacity to support a particular pair of steady states observed experimentally. In this article, hypothetical examples are used to illustrate the scope, purpose and methodology of this theory. The examples also demonstrate the way in which even partial multiple steady-state data provide a basis for highly refined discrimination between very similar mechanisms. In a companion article, actual multiple steady-state data are used to discriminate between proposed mechanisms for ethylene hydrogenation on rhodium. A public computer program is available that will allow the user to apply the theory described in this article without knowledge of any underlying theory. (C) 2000 Elsevier Science B.V. All rights reserved.