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This paper introduces a novel type of query, what we name Spatio-temporal Pattern Queries (STP). Such a query specifies a spatiotemporal pattern as a sequence of distinct spatial predicates where the predicate temporal ordering (exact or relative) matters. STP queries can use various types of spatial predicates (range search, nearest neighbor, etc.) where each such predicate is associated (1) with an exact temporal constraint (a time-instant or a time-interval), or (2) more generally, with a relative order among the other query predicates. Using traditional spatiotemporal index structures for these types of queries would be either inefficient or not an applicable solution. Alternatively, we propose specialized query evaluation algorithms for STP queries With Time. We also present a novel index structure, suitable for STP queries With Order. Finally, we conduct a comprehensive experimental evaluation to show the merits of our techniques.