Resource-transition circuits (RTCs) and siphons are related to the deadlock problem and liveness control problem in Petri net models of automated manufacturing systems. This paper will concentrate on a particular type of Petri nets called systems of sequential processes with resources (S3PRs) and solves the RTC and siphon enumeration problems. A graph-based technique is first used to find all elementary RTC structures. Any RTC can be expressed as a union of some elementary RTCs. Then, an iterative method is developed to recursively construct all maximal perfect-resource-transition circuits (MPCs), which can lead the system to deadlock, from the elementary RTCs. Finally, by the one-to-one correspondence between strict minimal siphons and MPCs, a new algorithm is obtained to compute strict minimal siphons in S3PRs.