This paper presents the first mathematical model simulating the recently discovered oscillatory behavior during CO oxidation on a Ni foil in a continuous-flow catalytic reactor. These oscillations occur in the presence of excess CO; thus, the well-known Sales-Turner-Maple model, simulating oscillations in oxygen excess, cannot be applied. We suggest a modification of the Sales-Turner-Maple model by introducing the precursor-mediated adsorption of CO. This made it possible to simulate the oscillations under reducing conditions. The suggested microkinetic model coupled with a continuous-flow reactor model predicts that the oscillations proceed on the partially oxidized catalyst because of the periodic formation and reduction of the surface oxide. The introduction of oxygen diffusion into the subsurface layers allows the description of the experimentally observed variation in Ni color during the oscillatory cycle. The developed model successfully reproduces experimental data as the temperature range of the oscillations together with their shape and amplitudes. (C) 2019 Elsevier Ltd. All rights reserved.