The paper considers a discrete-time continuous-variable autonomous system for which only a quantized state measurement [x(k)] is available. The problem is to set up a qualitative model that for a given quantized initial state [x(0)] describes the sequence of quantized states [x(k)]. First it is shown that the relation between [x(0)] and [x(k)] is ambiguous. Hence, the qualitative model is nondeterministic. Second, necessary and sufficient conditions are derived under which nondeterministic or stochastic automata represent qualitative models of a linear autonomous system. The results are illustrated by an oscillator.