A data processing system 2 includes multiple out-of-order issue queues 8, 10. A master serialization instruction MSI received by a first issue queue 8 is detected by slave generation circuitry 24 which generates a slave serialization instruction SSI added to a second issue queue 10. The master serialization instruction MSI manages serialization relative to the instructions within the first issue queue 8. The slave serialization instruction SSI manages serialization relative to the instructions within the second issue queue 10. The master serialization instruction MSI and the slave serialization instruction SSI are removed when both have met their serialization conditions and are respectively the oldest instructions within their issue queues.