Presented in this paper is an algorithmic procedure for resolving 'multiple conflicts' in Petri-net models of flexible assembly systems (FASs). An FAS constitutes an important part of a CIMS and is conveniently modelled with Petri nets. The 'flexibility' of an FAS appears as 'multiple conflicts' in a Petri-net model of the FAS. The proposed scheme for resolving multiple conflicts consists of three phases: identification of multiple conflict groups (MCGs) in a given Petri-net; identification of concurrently firable sub-sets (CFSSs) in each MCG; and determination of a to-be-fired transition set (FTS) based on a quantified priority scheme. Based on the proposed conflict resolution scheme, a Petri-net executor (PNE) was developed and a computer simulation of a simple flexible assembly line was performed.