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The goal of this work is to provide accurate dynamical models of oscillations in the flow past a rectangular cavity, for the purpose of bifurcation analysis and control. We have performed an extensive set of direct numerical simulations which provide the data used to derive and evaluate the models. Based on the method of Proper Orthogonal Decomposition (POD) and Galerkin projection, we obtain low-order models (from 6 to 60 states) which capture the dynamics very accurately over a few periods of oscillations, but deviate for long time.