In this paper we present a semantic model that is used to interpret a logic that represents concurrent actions having temporal extent. In an earlier paper [Pelavin and Allen, 1986] we described how this logic is used to formulate planning problems that involve concurrent actions and external events. In this paper we focus on the semantic structure. This structure provides a basis for describing the interaction between actions, both concurrent and sequential, and for composing simple actions to form complex ones. This model can also treat actions that are influenced by properties that hold and events that occur during the time that the action is to be executed. Each model includes a set of world-histories, which are complete worlds over time, and a function that relates world-histories that differ solely on the account of an action executed at a particular time. This treatment derives from the semantic theories of conditionals developed by Stalnaker [Stalnaker, 1968] and Lewis [Lewis, 1973].