We define timed automata with deadlines (TAD) which are a class of timed automata where time progress conditions depend on deadlines associated with transitions. We show that using TAD makes urgency specification easier. We present the model of Petri nets with deadlines (PND), which are (1-safe) Petri nets extended with clocks exactly as TAD are extensions of automata. We compare PND with different classes of timed Petri nets (TPNs) and show that safe TPNs can be modeled as PND. Some applications to modeling systems and in particular to modeling multimedia documents are presented