In this paper we introduce efficient parallel quadtree neighbor finding algorithms on hypercube multiprocessors. We observe that most existing parallel quadtree neighbor finding algorithms regard quadtree nodes only as combinatorial objects. Therefore, the restoration of geometric relations requires extra data movements and communication overhead by either sorting the quadtree nodes or traversing the embedded quadtree. Our approach considers the quadtree nodes as both combinatorial objects and geometric entities with spatial adjacency relations. By requiring the preserving of adjacency relations during the quadtree construction phase, we propose new parallel neighbor finding algorithms for finding edgeneighbors and corner-neighbors of all leaf nodes in a quadtree. Theoretical analysis and empirical testing are given to show that our algorithms are efficient and better than existing algorithms both in time and communication aspects.