Actor–event data are common in sociological settings, whereby one registers the pattern of attendance of a group of social actors to a number of events. We focus on 79 members of the Noordin Top terrorist network, who were monitored attending 45 events. The attendance or nonattendance of the terrorist to events defines the social fabric, such as group coherence and social communities. The aim of the analysis of such data is to learn about the affiliation structure. Actor–event data is often transformed to actor–actor data in order to be further analysed by network models, such as stochastic block models. This transformation and such analyses lead to a natural loss of information, particularly when one is interested in identifying, possibly overlapping, subgroups or communities of actors on the basis of their attendances to events. In this paper we propose an actor–event model for overlapping communities of terrorists which simplifies interpretation of the network. We propose a mixture model with overlapping clusters for the analysis of the binary actor–event network data, called $\mathtt{manet}$, and develop a Bayesian procedure for inference. After a simulation study, we show how this analysis of the terrorist network has clear interpretative advantages over the more traditional approaches of affiliation network analysis.