We analyze the kinetics of rapid bistable reactions (e.g., CO or hydrogen oxidation on Pt) occurring on a nm catalyst particle located inside a mesoscopic pore. Limitations for reactant diffusion inside a single pore are shown to modify the dependence of the reaction rate on the reactant pressures outside the pore. In particular, the position of the maximum reaction rate is shifted to higher CO pressures (provided that the O-2 pressure is fixed). This effect is significant if a pore is not too short. Similar effects are possible during oscillations in CO oxidation on supported nm catalyst particles.