This paper establishes a new class of dynamic games which incorporates two frequently observed real-life phenomena — durable strategies and uncertain horizon. In the presence of durable strategies and random horizon, significant modification of the dynamic optimization techniques is required to accommodate these phenomena. A novel dynamic optimization theorem is developed and a new set of equations characterizing a non-cooperative game equilibrium is derived. A subgame consistent solution for the cooperative game counterpart is obtained with a new theorem for the derivation of a payoff distribution procedure under random horizon and durable strategies. A number of new application results in dynamic games are derived to reflect practical considerations in making decision. Computational illustrations in an application involving a dynamic interactive investments game are provided.