Abstract: The resource-transition net (RTN) N_R is the reduction form of N, which is the Petri net model of an automated manufacturing system (AMS). Thus, N_R plays an important role in system deadlock analysis and control. After a couple of properties in resource-transition nets are summarized, conclusions are proposed as follows. If the inner sub-net N₁ on R₁ (where R₁ is an arbitrary resource subset) of the RTN N_R is strongly connected, there must be a resource-transition circuit (RTC) with R₁ as its resource set (such as θ=1,(·R₁∩R₁·)>). In addition, if θ satisfies the perfection condition, the RTC θ is a Perfect Maximal Resource-Transition Circuit (PMRTC) of N.