This paper presents efficient algorithms for updating moving octrees with real-time performance. The first algorithm works for octrees undergoing both translation and rotation motion; it works efficiently by compacting source octrees into a smaller set of cubes (not necessarily standard octree cubes) as a precomputation step, and by using a fast, exact cube/cube intersection test between source octree cubas and target octree cubes. A parallel version of the algorithm is also described. Finally, the paper presents an efficient algorithm for the more limited case of octree translation only. Experimental results are given to show the efficiency of the algorithms in comparison to competing algorithms. In addition to being fast, the algorithms presented are also space efficient in that they can produce target octrees in the linear octree representation.