The analysis of the formation and evolution of networks over time is of fundamental importance to social science, biology, and many other fields. While longitudinal network data sets are increasingly being recorded at the granularity of individual time-stamped events, most studies only focus on collapsed cross-sectional snapshots of the network. In this paper, we introduce a dynamic egocentric framework that models continuous-time network data using multivariate counting processes. For inference, an efficient partial likelihood approach is used, allowing our methods to scale to large networks. We apply our techniques to various citation networks and demon- strate the predictive power and interpretability of the learned statistical models.