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Summary form only given. When simulating hybrid discrete-continuous dynamical systems a key problem is the discontinuous model behavior. The state derivatives may change in a discontinuous way depending on the discrete state of the model. Conventional simulation algorithms are not suitable to integrate such hybrid system models with high accuracy and reasonable computational effort. In this paper we present results obtained with the simulation tool HYSIM we are developing. HYSIM can efficiently and accurately simulate hybrid systems including state and time events and sliding modes.