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In this paper, we study a new type of spatial query, Nearest Surrounder (NS), which searches the nearest surrounding spatial objects around a query point. NS query can be more useful than conventional nearest neighbor (NN) query as NS query takes the object orientation into consideration. To address this new type of query, we identify angle-based bounding properties and distance-bound properties of Rtree index. The former has not been explored for conventional spatial queries. With these identified properties, we propose two algorithms, namely, Sweep and Ripple. Sweep searches surrounders according to their orientation, while Ripple searches surrounders ordered by their distances to the query point. Both algorithms can deliver result incrementally with a single dataset lookup. We also consider the multiple-tier NS (mNS) query that searches multiple layers of NSs. We evaluate the algorithms and report their performance on both synthetic and real datasets.