This paper presents an extension of Petri net framework with imprecise temporal properties. We use possibility theory to represent imprecise time by time-stamping tokens and assigning durations to firing of the transitions. A method for approximation of an arbitrary temporal distribution with a set of possibilistic intervals is used to introduce the composition operation for two possibilistic temporal distributions. We developed a method to determining an effective enabling time of a transition with incoming tokens with possibilistic distributions. The utility of the proposed theory is illustrated using an example of an automated manufacturing system. The proposed approach is novel and has a broad utility beyond a timed Petri network and its applications. Keywords Petri nets, possibility theory, possibilistic temporal intervals, temporal composition.