A bus for coupling a plurality of units in a data processing system for the transfer of information therebetween. The units are coupled in a priority arrangement which is distributed, thereby providing priority logic in each of the units and allowing bus transfer cycles to be generated in an asynchronous manner. Priority is normally granted on the basis of physical position on the bus, highest priority being given to the first unit on the bus and lowest priority being given to the last unit on the bus. Each of the units includes priority logic which includes logic elements for requesting a bus cycle, such request being granted if no other higher priority unit has also requested a bus cycle. The request for and an indication of the grant of the bus cycle are stored in each unit so requesting and being granted the bus cycle respectively; only one such unit is capable of having the grant of a bus cycle at any given time, whereas any number of such units may have their requests pending at any particular time. The present invention provides a modification to the priority logic which allows a lowest priority unit to be physically positioned at other than the last unit position on the common bus.