This paper presents an algorithm for exact contact prediction between moving objects bounded by curved surfaces. The algorithm uses hierarchies of oriented bounding boxes (HOBBs) and local numerical methods for finding contact. Objects need not be convex and are described using the B-rep scheme. The bounding faces are represented by nonuniform rational B-splines (NURBS). The collision time is sought in short time intervals during the motion, during which time is one of the problem variables. HOBBs are based on curvature regions of the surfaces. This criterion ensures that local numerical methods will converge to the contact points if they exist. The patches enclosed in overlapping leaf nodes are tested for contact by solving a system of nonlinear equations, based on the type of collision expected. The types of collision studied are cusp–cusp, cusp–ridge, cusp–
face, ridge–ridge, ridge–face, and face–face collisions. The current algorithm is implemented and compared to an efficient polyhedral collision package, and results appear promising.