Two stochastic models for the spread of an infection through a heterogeneous population are considered. First, we consider a model where the incubation period has an increasing hazard rate but constant infectiousness; in the second model, the incubation period is the sum of p exponentially distributed stages, each with its own mean and level of infectiousness. By using multitype birth-death and branching processes as approximations to each epidemic model, it is shown that the epidemics initially have underlying exponential growth. Furthermore, the growth rate ? is an increasing function of the Frobenius root of the matrix of reproductive ratios Ro. The results have applications in long-term sensitivity analyses, model fitting, and the determination of optimal vaccination strategies. © 1990 Oxford University Press.