Each packet message in a sequence of packet messages is sent with an associated packet message priority label in accordance with a predetermined cyclic sequence of such labels. These priority labels each represent one of a plurality of priority levels and the position of each label in the cyclic sequence is such that number of consecutive lower priority labels between that label and the nearest label of equal or higher priority is substantially maximized. In this way, if packet messages are dropped from the sequence due to congestion on a priority basis, the packet messaging method and apparatus according to the invention ensure that, as far as possible, regular update packet messages are still received from all packet message sources.