The study of spatial variations in disease rates is a common epidemiological approach used to describe geographical clustering of disease and to generate hypotheses about the possible `causes' which could explain apparent differences in risk. Recent statistical and computational developments have led to the use of realistically complex models to account for overdispersion and spatial correlation. However, these developments have focused almost exclusively on spatial modelling of a single disease. Many diseases share common risk factors (smoking being an obvious example) and if similar patterns of geographical variation of related diseases can be identified, this may provide more convincing evidence of real clustering in the underlying risk surface. In this paper, we propose shared component models for the joint spatial analysis of two diseases. The key idea is to identify shared and disease-specific spatially-varying latent risk factors by appropriate partitioning of the underlying risk surface for each disease. The various components of this partition are modelled simulataneously using nonparametric cluster models implemented via reversible jump Markov chain Monte Carlo methods. We illustrate the methodology through an analysis of oral and oesophageal cancer mortality in the 544 districts of Germany, 1986-1990.