We present a formalism for representing the intentions of agents engaged in cooperative planning and acting. We focus on cases where one agent alone cannot accomplish a complex task and must subcontract with other agents. Evolving intentions over time during the planning and acting, and the conditions under which an agent can adopt and maintain an intention, are central. In particular, the time taken to plan and to subcontract are modeled explicitly in the logic. This explicit time-representation is used to account for the time it takes an agent to adopt an intention. We use a syntactic approach presenting a formal logical calculus that can be regarded as a meta-logic that describes the reasoning and activities of the agents. We write some of the axioms of this meta-language and explain the minimal model semantics, in which one model, the intended model, represents the actual beliefs, intentions, and actions of the agents. We also prove several results showing that under the appropriate conditions the agents will act as expected.