The principal-agent paradigm, in which a principal has a primary stake in the performance of some system but delegates operational control of that system to an agent, has many natural applications in operations management (OM). However, existing principal-agent models are of limited use to OM researchers because they cannot represent the rich dynamic structure required of OM models. This paper formulates a novel dynamic model that overcomes these limitations by combining the principal-agent framework with the physical structure of a Markov decision process. In this model one has a system moving from state to state as time passes, with transition probabilities depending on actions chosen by an agent, and a principal who pays the agent based on state transitions observed. The principal seeks an optimal payment scheme, striving to induce the actions that will maximize her expected discounted profits over a finite planning horizon. Although dynamic principal-agent models similar to the one proposed here are considered intractable, a set of assumptions are introduced that enable a systematic analysis. These assumptions involve the “economic structure” of the model but not its “physical structure.” Under these assumptions, the paper establishes that one can use a dynamic-programming recursion to derive an optimal payment scheme. This scheme is memoryless and satisfies a generalization of Bellman’s principle of optimality. Important managerial insights are highlighted in the context of a two-state example called “the maintenance problem”.