We present novel algorithms for updating bounding volume hierarchies of objects undergoing arbitrary deformations. Therefore, we introduce two new data structures, the kinetic AABB tree and the kinetic BoxTree. The event-based approach of the kinetic data structures framework enables us to show that our algorithms are optimal in the number of updates. Moreover, we show a lower bound for the total number of BV updates, which is independent of the number of frames. We used our kinetic bounding volume hierarchies for collision detection and performed a comparison with the classical bottomup update method. The results show that our algorithms perform up to ten times faster in practically relevant scenarios. CR Categories: I.3.5 [Computing Methodologies]: Computational Geometry and Object Modeling—Geometric algorithms, Object hierarchies; I.3.7 [Computing Methodologies]: ThreeDimensional Graphics and Realism—Animation, Virtual reality