A pipeline processing apparatus for performing processing operations in a succession of processing cycles, in which each cycle is composed of a succession of stages that include an instruction decoding stage for decoding an instruction associated with the cycle and an execution stage for executing an operation dependent on the instruction, and the processing cycles include a first cycle which starts at a first time and a second cycle that begins at a second time that is after the first time and that overlaps the first cycle in time. The apparatus is constructed and controlled for causing a branch instruction to be decoded in the instruction decoding stage of the first cycle; and for effecting a calculation in the execution stage of the first cycle, dependent on the branch instruction decoded in the instruction decoding stage of the first cycle.