The paper, which employs damping torque concepts associated with frequency response analysis, considers the co-ordinated design of power system stabilisers (PSSs) in multimachine power systems. It endeavours to extend to the multimachine environment some of the earlier work which was applied to the analysis of the single machine case, and which provided an insight into the action of the stabiliser. The aim of the proposed approach is to provide, through the action of the stabiliser, an electrical damping torque proportional to speed perturbations, i.e. ΔPei(s) =DiΔωi(s). The stabiliser network is designed to compensate for the phase lag and gain in the machine/system transfer function ΔPei(s)/Δvri(s). The stabiliser gainDiis coordinated, in the first instance, so that the damping effect is distributed among those machines fitted with stabilisers in proportion to their ratings. The damping performance of a sample power system with PSSs installed is shown to be comparable to that for a multimachine system without PSSs in which a pure damping torque is introduced artificially in the transfer function block representing shaft dynamics. Owing to machine interaction, however, an additional left shift of certain oscillatory modes is shown to be due to an electrical damping torque introduced on machineithrough the action of the PSS on machinej.