The paper deals with the discrete-event modelling of continuous-variable dynamical systems whose input and state signals can only be measured through quantisers. A change of the quantised input or state value is called an input or a state event. The paper concerns the general case in which these events may occur asynchronously to one another. A nondeterministic automaton is used as the discrete-event model of such quantised systems. The paper presents an abstraction algorithm for determining the state transition relation of the automaton from the state-space description of the continuous-time continuous-variable system and the signal space partitions introduced by the quantisers. The abstraction is based on the reachability analysis of quantised systems. A hierarchy of models with respect to the set of spurious behaviours is obtained by varying an abstraction parameter. The discrete-event models are proved to be complete models of the quantised system with the best possible transition relation.