Evaluation of complex event queries over time involves storing information about those events that are relevant for, i.e., might contribute to, future answers. We call the period of time for which an event or an intermediate result must (at least) be stored its temporal relevance. This paper pioneers a precise definition of temporal relevance and develops a method for statically (i.e., at compile time) determining it. During query evaluation (i.e., at run time), this enables garbage collection of events that become irrelevant as time progresses. Temporal relevance is also important at compile time for cost-based query planning. Categories and Subject Descriptors