This paper shows how to use the Petri Net with Stacks (PNS-net) to express asynchronous concurrent distributed computing systems (DCS) which are based on the environment of loosely coupled computing systems, and puts forth method to detect types of DCS deadlocks such as Cycle Waiting, Hold and Wait, Exclusive access, etc. Then we can apply the algorithm that this paper narrates which actually changes PNS-net into production rules during the system-designing stages. By designing a diagnosis system for automatic detection of deadlocks in asynchronous concurrent distributed computing systems (ACDCS), the goal of this paper is to develop and approach for reducing the time and cost in the software development.