The paper presents a novel control-oriented, first-principle model of a three-way catalytic converter (TWC). The model accurately predicts the air-fuel ratio downstream of the catalyst and provides insights into the relative oxygen level (ROL) profile along the catalyst. The reaction mechanism of the TWC model is simplified to only two reactions, with oxygen being the only species stored on the active surface of the catalyst. All the information about the gas composition is taken from the upstream wide-range oxygen sensor. Additional model inputs are the exhaust gas temperature and the exhaust mass flow. The model is parameterized with only a few measurements from an engine test bench. Exact values of gas concentrations are not needed at any point. The ROL profile is a good indicator for the condition of the TWC. It can therefore be used to derive optimal TWC depletion strategies after fuel cut-off phases. Since the model is real-time capable, the ROL profile can even be used for on-line control strategies. Based thereon, a causal strategy is proposed with results that match those of the non-causal strategies found in off-line optimizations. (C) 2012 Elsevier Ltd. All rights reserved.