Real-world relational data sets, such as social networks, often involve measurements over time. We propose a Bayesian nonparametric latent feature model for such data, where the latent features for each actor in the network evolve according to a Markov process, extending recent work on similar models for static networks. We show how the number of features and their trajectories for each actor can be inferred simultaneously and demonstrate the utility of this model on prediction tasks using synthetic and real-world data. 1