This paper addresses the structural change in a local urban housing market within a submarket framework. There is a voluminous literature examining the economic structure and operation of urban housing submarkets, with much of the associated empirical work based on static cross-sectional studies. Analysis of the temporal dynamics of local markets has tended to be perfunctory. As such, our understanding of structural change over time remains underdeveloped. In this paper we construct repeat-sale indices at the urban submarket level and deploy cointegration analysis to examine the stability of spatially defined housing submarkets within Glasgow between 1984 and 1997. Specifically, we consider whether price differences between submarkets have been eroded by a process of arbitrage operating through supply-side responses and/or migration flows. The empirical analysis shows that a stable system of housing submarkets persists throughout the study period.