The paper is devoted to the experimental and theoretical studies of self-sustained oscillations and wave phenomena during CO oxidation on Ni foil. A new type of spatial structures arising due to the redox processes of the catalyst and observed under isothermal conditions at atmospheric pressure were studied. A 3D distributed mathematical model was constructed, which describes the color change and the propagation of kinetic waves of nickel oxidation–reduction in a flow-through reactor. The main reason for the wave phenomena and their propagation during CO oxidation on nickel was shown to be the presence of an oxygen concentration gradient in the flow-through reactor due to the effect of mass transfer on the reaction rate.