In a data processing system in which resource units are shared by a plurality of processing units, an arbitration unit is disclosed wherein the priority assigned to each processing unit is dynamically assigned to equalize accessibility to the shared resource. A signal path, associated with each possible level of priority, is coupled to each processor unit. The processor unit applies an activation signal to the signal line associated with the priority of the processing unit when the processing unit has a requirement for the shared resource and an arbitration is being performed to determine access to the resource. During the arbitration procedure, each processing unit requiring access to the shared resource compares the current priority of the associated processing unit to the activation signals on the signal paths to determine when the processing unit can gain access to the shared resource. After the arbitration procedure, the processing unit priority level is redetermined by each processing unit based on a comparison of the current priority level and the highest priority level active during arbitration.