This paper presents a parallel algorithm to execute Petri nets with time, enforcing the even progression of internal time with respect to that of the real time and allowing the exchange of information with the environment. We define a class of Petri nets suitable for a parallel execution machine which preserves the step sequence semantics of the nets and ensures time consistent executions while taking into account the solicitation of its environment. The question of the efficient verification of such nets has been addressed in a separate paper (see [F. Pommereau, Causal Time Calculus, FORMATS'03. LNCS 2791, Springer, 2004.]), the present one is more focused on the practical aspects involved in the execution of so modelled systems.