The paper concerns process supervision tasks in which a continuous-variable system has to be moved into a globally defined final state. A hybrid model is proposed that describes the discrete-event behaviour as well as the quantitative behaviour of the continuous-variable system. The model consists of a Petri net and of differential equations whose validity depends on the marking of the net. The supervisory control task is solved by searching for a path within the Petri net from the current towards the final state and by using the relevant quantitative models to determine the speed of the state transitions. The results are illustrated by means of a laboratory lank system. (C) 2000 Elsevier Science Ltd. All rights reserved.