The objective of viral marketing is to utilize existing social interactions between customers for world--of--mouth advertising of products. In order to design effective marketing strategies, one needs to understand how influence is propagated across such social networks. Here we study a simple influence propagation process in a network composed of two loosely coupled communities. We find that for a certain range of network parameters, the dynamics of the influence propagation is characterized by a doubly--critical behavior. Our results also suggest that the presence of the community structure, or network modularity, might have important implications for choosing appropriate marketing strategies.