A global kinetic model is developed for the co-oxidation of CO and C3H6 over a Pt/Al2O3 diesel oxidation monolithic catalyst based on a recent bench flow reactor study (Abedi et al., 2012). A monolith reactor model containing these kinetics is used to elucidate the dynamic and steady state hysteresis behavior observed during oxidation of a CO + C3H6 mixture on Pt/Al2O3. Dynamic hysteresis is observed during temperature-programmed oxidation which involves ramping the feed gas temperature up and down at a constant ramp rate. The predicted solid temperature spatial profile during ramp-up and ramp-down shows how the catalyst temperature lags behind the inlet temperature change, especially during the ramp-down. The dynamic hysteresis loop, whose width increases with the ramp rate and effective heat Peclet number (Pe(h,eff)), is mainly a result of disparate time scales of thermal front propagation and temperature ramp and will be present even for reactions with negligible heat release. Steady state hysteresis can also be explained based on adiabatic temperature rise (Delta T-ad) and Pe(h,eff), i.e. thermokinetic multiplicity. The region of steady state hysteresis loop expands with an increasing Delta T-ad which is proportional to the feed concentrations of CO and C3H6. For fixed Delta T-ad, the steady state multiplicity disappears as Pe(h,eff) increases or when there is negligible thermal feedback due to intra or interphase heat transfer. Finally, the model is used to construct a map that may be used to assess the light-off features of multiple reaction systems in monolith reactors. (C) 2015 Elsevier B.V. All rights reserved.