  In this paper we study a simple cascading process in a structured
heterogeneous population, namely, a network composed of two loosely coupled
communities. We demonstrate that under certain conditions the cascading
dynamics in such a network has a two--tiered structure that characterizes
activity spreading at different rates in the communities. We study the dynamics
of the model using both simulations and an analytical approach based on
annealed approximation, and obtain good agreement between the two. Our results
suggest that network modularity might have implications in various
applications, such as epidemiology and viral marketing.
