Group communication is the core of societal interactions. Therefore, artificial agents should be able to communicate with groups as well as individuals. However, most contem-porary agent communication languages, notably FIPA and KQML, have either no provision or no well-defined seman-tics for group communication. We give a semantics for group communication that we believe can profitably enrich the agent communication languages. In our semantics, indi-vidual communication is a special case of group communication wherein each communicating group consists of a single agent. One of the novel features of this semantics is that it allows senders to send messages even without knowing all the potential recipients of those messages -- a typical scenario in broadcast communication.