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This paper develops a dynamic model of the urban residential market. Under specific assumptions about market behavior on both the supply and the demand sides it is shown that cities grow by attaining a sequence of short run equilibria. A set of recursive equations is derived and through these the impact of growth on the structure of rents, densities, and consumer welfare is analyzed. The dynamic model explains the decay of the central locations in large old American cities. Housing obsolescence and abandonment arises under special conditions and is reflected in positively sloped rent gradients in central locations. The well-known static result of declining densities with distance from the center is shown to occur only under special conditions such as rising income levels. Directions for further analyzing urban growth, by expanding this dynamic approach, are pointed out.