This paper is concerned with specifying and proving correct systems in which time appears as a parameter. We model such systems via Merlin's Time Petri Nets. An enumerative analysis technique is introduced for these nets based on the computation of a set of state classes and a reachability relation on the set. State classes are defined in the text and an algorithm is provided for their enumeration. This enumerative approach allows us to derive a finite representation of their behavior for a large family of Time Petri Nets. The analysis method is illustrated by the analysis of a communication protocol.