Significant efforts have gone into the development of statistical models for analyzing data in the form of networks, such as social networks. Most existing work has focused on modeling static networks, which represent either a single time snapshot or an aggregate view over time. There has been recent interest in statistical modeling of dynamic networks, which are observed at multiple points in time and offer a richer representation of many complex phenomena. In this paper, we propose a state-space model for dynamic networks that extends the well-known stochastic blockmodel for static networks to the dynamic setting. We then propose a procedure to fit the model using a modification of the extended Kalman filter augmented with a local search. We apply the procedure to analyze a dynamic social network of email communication.