%B Proc. 40th IEEE Conf. on Decision and Control %X We establish equivalences among five classes of hybrid systems, that we have encountered in previous research: mixed logical dynamical systems, linear complementarity systems, extended linear complementarity systems, piecewise affine systems, and max-min-plus-scaling systems. These results are of paramount importance for transferring properties and tools from one class to another %C Orlando, Florida USA, December 2001 %L eprints583 %A W.P.M.H. Heemels %A Bart De Schutter %A Alberto Bemporad %P 364-369 %I IEEE %T On the equivalence of classes of hybrid dynamical models %V 1 %J Proc. 40th IEEE Conf. on Decision and Control %R 10.1109/.2001.980127 %D 2001 %K hybrid dynamical models; linear complementarity systems; max-min-plus-scaling systems; mixed logical dynamical systems; piecewise affine systems; continuous time systems; discrete systems; linear systems