Longitudinal network data recording the moment at which ties appear, change, or disappear are increasingly available. Event history models can be used to analyze the dynamics of time-stamped network data. This paper adapts the discrete-time event history model to social network data. A discrete-time event history model can easily incorporate a multilevel design and time-varying covariates. A multilevel design is needed to account for dependencies among ties and vertices, which should not be ignored in a small longitudinal network. Time-varying covariates are required to analyze network effects, that is, the impact of previous ties. In addition, a discrete-time event history model handles constraints on who can act or who can be acted upon in a straightforward way. The model can be estimated with multilevel logistic regression analysis, which is illustrated by an application to book reviews, so network evolution can be analyzed with a fairly standard statistical tool.Keywords: network dynamics; discrete-time event history models; multilevel logistic regression analysis; longitudinal social networks; book reviewing.In the analysis of longitudinal social networks, relatively little attention has been paid to the timing of relational events, namely the moments at which ties appear, change, or disappear. Initially, this kind of data was not available because longitudinal data were collected by means of repeatedly administered surveys (Katz and Proctor 1959: 318; Runger and Wasserman 1979: 144). As a consequence, models for network dynamics