A theoretical analysis is made of the long-period (phugoid) oscillations of a lifting vehicle in hypersonic flight up to and including orbital speeds in any atmosphere. These oscillations correspond to a direct exchange between the kinetic energy and the potential energy along an oscillating flight path governed primarily by the trimmed steady-state zero pitching moment. The expressions derived for the period and damping of these oscillations show that for all speeds near or greater than sonic the atmospheric density gradient has an important effect in decreasing the period and increasing the damping of the phugoid oscillations. As orbital speeds are approached, it is found that the decrease in gravitational attraction with altitude overcomes the effect of the decrease in atmospheric density with altitude so that with increasing speed the phugoid period asymptotically approaches the corresponding satellite orbit period. In addition, simple explicit expressions are derived for the so-called "short period" or angle-of-attack oscillations. These and the phugoid relations are shown to be in excellent agreement with the numerical calculations previously presented by Etkin.