Handling of loops in processors

A processor is capable of executing a software-pipelined loop. A plurality of registers (20) store values produced and consumed by executed instructions. A register renaming unit (32) renames the registers during execution of the loop. In the event that a software-pipelined loop requires zero iterations, the registers are renamed in a predetermined way to make the register allocation consistent with that which occurs in the normal case in which the loop has one or more iterations. This is achieved by carrying out an epilogue phase only of the loop with the instructions in the loop schedule turned off so that their results do not commit. The issuance of the instructions in the epilogue phase brings about the predetermined renaming automatically. The number of epilogue iterations may be specified in a loop instruction used to start up the loop.