Optimising trafic signal timings for a multiple-junction road network is a difficult but important problem. The essential difficulty of this problem is that the traffic signals need to coordinate their behaviours to achieve the common goal of optimising overall network delay. This paper discusses a novel approach towards the generation of optimal signalling strategies, based on the use of a genetic algorithm (GA). This GA optimises the set of signal timings for all junctions in network. The different efficient red and green times for all the signals are determined by genetic algorithm as well as the offset time for each junction. Previous attempts to do this rely on a fixed cycle time, whereas the algorithm described here attempts to optimise cycle time for each junction as well as proportion of green times. The fitness function is a measure of the overall delay of the network. The resulting optimised signalling strategies were compared against a well-known civil engineering technique, and conclusions drawn.