1. In a computer system having a main memory containing instructions, some of which are conditional branch instructions, a conditional branch instruction having a first and a second sequence of instructions defining a first and second path respectively following said conditional branch instruction, and having a processor for processing instructions, a prefetcher for prefetching instructions before they are requested by the processor, a cache memory for storing prefetched instructions and a memory device for storing indicia relating to the location of instructions in the main memory which may have to be processed by the processor, a method of maintaining instructions in the cache memory comprising the steps of: prefetching instructions and identifying any prefetched instructions that correspond to a conditional branch instruction; if a prefetched instruction is a conditional branch instruction, continuing to prefetch instructions from one of either the first or second path following the conditional branch instruction and storing in the memory device, indicia relating to the location of the first instruction of the other of the first and second paths; storing in the memory device indicia corresponding to the location relating to the instruction last prefetched and prefetching instructions sequentially beginning with the address of the instruction stored in the memory device; and when it has been determined that instruction addresses stored in the memory device are no longer in the path of instructions to be executed, nullifying addresses from the memory device that are no longer in the path of execution.