Databases of moving objects are important for air traffic control, ground traffic, and battlefield configurations. We introduce the (historical and spatial) range close-pair query for moving objects as an important problem for such databases. The purpose of a range close-pair query for moving objects is to find pairs of objects that were closer than during time interval I and within spatial range R, where , I and R are user-specified parameters. This paper solves the range close-pair query using two components: the retrieval component and the close-pair identification component. The retrieval component breaks up long trajectories into trajectory segments, which are produced in increasing time order, without the need for sorting. The retrieval component takes advantage of a new index mechanism, the Multiple TSB-tree. The segments are then pipelined to the close-pair identification component. The identification component introduces a novel spatial sweep that sweeps by time and one spati...