A microprocessor pipeline arrangement 1 includes a plurality of functional units P1, P2, P3, . . . , PN. A number of the functional units P1, P3, PN have access to a respective cache memory C1, C3, CN from which it can retrieve data needed to process threads that pass through the pipeline. The pipeline arrangement 1 also includes a number of monitors to determine when the system enters a state of livelock (e.g. inter-cache livelocks, intra-cache livelocks and/or “near-livelock” situations): a top-level monitor MT to detect livelock situations in the pipeline as a whole; and second-level (“local”) monitors M1 and M3 associated with individual caches C1 and C3.If the system is determined to have entered a livelock state, e.g. by the top-level monitor MT, the number of threads able to change the contents of one or more of the caches C1, C3, CN is reduced.