The paper concerns linear continuous-variable systems whose state can be measured only through a quantiser. As for an observer the system together with the quantiser behaves like a discrete-event system, the problem of representing this system by some deterministic finite state machine is considered. The main difficulty of this representation problem occurs due to the nondeterminism introduced by the state quantisation. It is investigated under what conditions on the linear continuous-variable system and on the state quantisation the discrete-event behaviour is deterministic. The main results are sufficient conditions for this property.