A numerical analysis is presented to explain the effect of catalytic surfactant on roughness evolution during film growth mediated by an electrochemical or chemical reaction. The analysis uses the previously published curvature enhanced accelerator coverage (CEAC) mechanism; the CEAC mechanism accounts for the conservation of local coverage of adsorbed catalyst on a deforming interface. It has recently been demonstrated that the CEAC mechanism stabilizes surfaces against the growth of instabilities when the coverage of an adsorbed catalyst is in a steady state governed by catalyst consumption balanced by accumulation from the ambient. Surfaces with global conservation of catalyst during deposition, i.e., experiencing neither accumulation nor consumption, are not predicted to be stable. Experimental evidence suggests otherwise. This paper uses numerical analysis to demonstrate that such surfaces, while not strictly stable to arbitrarily small perturbations, are effectively stabilized through the formation of time dependent oscillatory states with extremely small amplitudes. A simple front tracking algorithm is used to model the evolution of the interface. (C) 2004 The Electrochemical Society.