A computer system for executing branch instructions and a method of executing branch instructions are described. Two instruction fetchers respectively fetch a sequence of instructions from memory for execution and a sequence of instructions commencing from a target location identified by a set branch instruction in a sequence of instructions being executed. When an effect branch signal is generated, the target instructions are next executed, and the fetcher which was fetching the instructions for execution commences fetching of the target instructions. The effect branch signal is generated separately from the set branch instruction. In another aspect, the effect branch signal is generated on execution of a conditional effect branch instruction, located at the point in the instruction sequence where the branch is to be taken.