A stochastic computational method developed for analysis of two-state cross-bridge models was extended and used to compute the oscillatory movement generated by three-state cross-bridge models containing a rate function proportional to ATP concentration. Only one of the possible three-state models appears satisfactory; with this model, the frequency of oscillation, at constant amplitude, responds to changes in both ATP concentration and viscosity in the same way as real flagella. In this model, ATP binding causes cross-bridge detachment, which is rate limiting at low ATP concentrations; while at high ATP concentrations a transition between two attached states limits the rate of cross-bridge detachment. Since this model agrees with observations on actomyosin ATPase kinetics, the data on flagellar oscillation frequency support the idea that the movement-generating mechanisms of flagella and muscle are similar.