The method of singular perturbations is applied to the determination of the optimal range-fuel-time trajectory for an air-breathing missile. This method is shown to lead to the reduced-order "cruise-dash" model, and this model is used in the optimization study. Earlier work in this area is extended by the inclusion of two not heretofore considered limits on the dynamical system. The results of the earlier work are shown to hold throughout much of the velocity regime in which the missile operates, but operation in the very high and very low velocity ranges is shown to be sharply curtailed, with the optimal operating points being changed drastically in some cases. Also, the effect of the non-zero minimum admissible throttle setting and the resultant throttle-chattering on the solution of the control problem is examined in some detail. / M.S.