Estimates of maximum amplitudes of conductor galloping are needed in order to determine appropriate phase-to-phase clearances of overhead power lines. A new method for computing these estimates is obtained by the use of mathematical models of conductor galloping that include both vertical and torsional motion. The method gives estimates of the maximum gallop amplitude and frequency for various wind speeds. The stability of the predicted gallop limit cycle is determined by perturbation of the limit cycle parameters. Computer simulations show good agreement with the maximum amplitude and frequency estimates predicted by the model. The maximum gallop amplitudes predicted by the model also conform well with those observed on actual galloping lines. In addition, this analysis verifies what a number of galloping conductor researchers had long expected, namely, that torsional conductor motion limits maximum gallop amplitudes. © 1991.