Studying the kinetics of CO oxidation over Pd foil at elevated CO and O2 pressures, we observed an inverse hysteresis: CO conversion was much lower under sample cooling than under foil heating. It was established that under heating the oxidation of metallic palladium to bulk palladium oxide occurred through formation of the palladium surface oxide. Under cooling the bulk oxide reduced directly to metallic species, and in this case some self-sustained oscillations of reaction rate were observed. The catalytic scheme including main various oxygen states of the palladium surface and bulk with transitions between them under reaction conditions in heating/cooling catalytic cycle was proposed. On the base of this scheme the kinetic model of CO oxidation reaction was developed. Both most important mechanisms: Langmuir - Hinshelwood and Mars - van Krevelen, were involved for description of the observed kinetic nonlinear phenomena. The performed simulations demonstrated the capability of this model to describe well the inverse hysteresis of CO oxidation rate together with its oscillatory behavior at constant temperature within the hysteresis loop.