A nonisothermal monolithic reactor model with a global kinetic formulation is developed to predict the steady-state and cyclic oxidation and reduction with CO and H-2 of a model three-way NOx storage catalyst (TWNSC). Data were used from a parallel experimental study conducted by Malamis et al. [1] along with kinetics measurements made in the current study. The reactor model comprises a low-dimensional treatment of the transport processes and multi-site NOx and O-2 storage combined with catalytic kinetics of the reaction steps. Kinetic sub-models of NO and CO single and co-oxidation are developed to capture the CO and NO light-off trends including inhibition effects. The sub-models are combined to simulate the catalyst performance under both steady-state and cyclic conditions. The TWNSC model predicts the steady-state product distribution spanning a range of rich conditions, along with cyclic operation features, including cycle-averaged NOx conversion and NH3 selectivity, and the transient species concentrations and temperature profiles over a wide range of total cycle time (TCT, 10 s-200 s) at 50% duty cycle rich. The model captures the key feature of the TWNSC using CO and H-2 as reductants. The results point to the importance of sizing the TWNSC for either NO reduction to N-2 or NH3 formation, depending on the application. The TWNSC reactor model provides insight about reaction and transport interactions, spatio-temporal features, etc., along with guidance in the catalyst design and operation strategy optimization.