Aleksandar Donev a,b, Salvatore Torquato a,b,c,*, Frank H. Stillinger c a Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA b Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, NJ 08540, USA c Department of Chemistry, Princeton University, Princeton, NJ 08540, USA Received in revised form 19 May 2004; accepted 9 August 2004 Available online 11 November 2004 Journal of Computational Physics 202 (2005) 765–793 Abstract We apply the algorithm presented in the first part of this series of papers to systems of hard ellipses and ellipsoids. The theoretical machinery needed to treat such particles, including the overlap potentials, is developed in full detail. We describe an algorithm for predicting the time of collision for two moving ellipses or ellipsoids. We present performance results for our implementation of the algorithm, demonstrating that for dense systems of very aspherical ellipsoids the novel techniques of using neighbor lists and bounding sphere complexes, offer as much as two orders of magnitude improvement in efficiency over direct adaptations of traditional event-driven molecular dynamics algorithms. The practical utility of the algorithm is demonstrated by presenting several interesting physical applications, including the generation of jammed packings inside spherical containers, the study of contact force chains in jammed packings, and melting the densest-known equilibrium crystals of prolate spheroids.