Models of dynamic networks - networks that evolve over time - have manifold applications. We develop a discrete-time generative model for social network evolution that inherits the richness and flexibility of the class of exponential-family random graph models. The model - a Separable Temporal ERGM (STERGM) - facilitates separable modeling of the tie duration distributions and the structural dynamics of tie formation. We develop likelihood-based inference for the model, and provide computational algorithms for maximum likelihood estimation. We illustrate the interpretability of the model in analyzing a longitudinal network of friendship ties within a school.