Many exothermic reactions, such as the oxidation of CO in a catalyst pellet may present multiplicity of steady states. Experimental results suggest this behavior in a copper ceria catalyst, and this in turn would indicate that the kinetics should be nonmonotonic with respect to reactants' compositions. The model for the reaction is described by a two-point boundary value problem that is hard to solve with direct methods, even when seeking a single solution. The aim of this work is to implement a homotopic method to find all the steady states of this kind of problems. The search for solutions is driven by a pseudo arclength continuation. Homotopic curves that passes through all possible solutions are obtained. Also, a study of the dependence of the initial point upon the curve is performed. (C) 2010 American Institute of Chemical Engineers AIChE J, 57: 473-481, 2011