Multistage carcinogenesis models describe the evolution of the cells in an individual's organ from a normal stage to a pre-neoplastic stage to a neoplastic stage. The triggers for the passage from one stage to the next one are presumed to be genetic alterations, which are not only governed by purely random events but also by individual environmental and genetic factors. We generalize existing models of carcinogenesis to populations composed of heterogeneous individuals, thus taking the environmental and genetic variability into account.