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The treatment of exogenous events in planning is practically important in many real-world domains where the preconditions of certain plan actions are affected by such events. In this paper we focus on planning in temporal domains with exogenous events that happen at known times, imposing the constraint that certain actions in the plan must be executed during some predefined time windows. When actions have durations, handling such temporal constraints adds an extra difficulty to planning. We propose an approach to planning in these domains which integrates constraint-based temporal reasoning into a graph-based planning framework using local search. Our techniques are implemented in a planner that took part in the 4th International Planning Competition (IPC-4). A statistical analysis of the results of IPC-4 demonstrates the effectiveness of our approach in terms of both CPU-time and plan quality. Additional experiments show the good performance of the temporal reasoning techniques integrated into our planner.