In this paper, a non-linear dynamic model is presented for a housing market in which various types of households and dwellings are distinguished. The model is based on a stock-flow framework, in which households have to cope with incomplete information when searching for dwellings. The model includes life-cycle patterns (social mobility, ageing) as well as stochastic dwelling preferences. Simulations are carried out with the model to investigate its properties (existence of stationary states, etc.) under various conditions of housing supply. Special attention is paid to vacancy rates, duration of residence, and length of vacancy chains.