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M. A j m o n e M a r s a n D i p a r t i m e n t o di Scienze dell' Informazione Universit£ di Milano, I t a l y A B S T R A C T -Petri nets in which random firing delays are associated with transitions whose firing is an atomic operation are known under the name "stochastic Petri nets". These models are discussed, with the purpose of ezplaining why they were proposed in the performance evaluation field, why random delays with negative ezponential probability density functions are mainly used, and what are their strong and weak points. An effort is made to summarize the lines of research that are currently being pursued~ and to ezplain what new results would be regarded as breakthroughs and have the most impact on the use of this modeling technique in the application field.