Considers the use of Petri nets for the study of the deadlock problem for two classes of kanban manufacturing systems: kanban flow lines and reentrant kanban flow lines. In the Petri net framework deadlock can be easily characterized by means of the siphon concept. The first result of the paper is the formal proof that kanban flow lines are deadlock free, regardless of the initial marking of the underlying Petri net. Vice versa, for the class of reentrant kanban flow lines, where resource sharing occurs, by means of simple examples we show that deadlock can actually occur. Formal results for the latter class are given, characterizing some fundamental properties of "critical" siphons i.e., siphons that may become empty leading to deadlock.