An MQ message has a priority associated with it. Normally, the value specified is between 0 (the minimum) and 9 (the maximum). However, it is possible to specify a value greater than 9.
An MQPUT() call specifying MQMD.Priority=77 will complete with the MQRC_PRIORITY_EXCEEDS_MAXIMUM warning reason code.
The message is treated by MQ as a priority 9 message, but the MQMD.Priority field is set to the supplied value, 77 .
If you consider another messaging provider product, A, whose priorities range from 0 to 99, then the MQ behaviour would allow MQ to preserve the original priority whilst transporting a message from one instance of A to another instance of A.