Approximate analytic solutions are obtained for the lifetimes of satellites in either circular or elliptical orbits under the influence of continuous tangential thrust, atmospheric drag, and planet oblateness. The cases treated are those in which the satellite mission requires the perigee of the orbit to remain within fixed bounds in altitude and position. For circular orbits it is found that, to increase greatly the useful life time over the nonthrusting case, an almost perfect matching of thrust to drag is required. Two solutions are obtained for elliptical orbits. The first requires that the thrust level over each revolution be the value needed to hold the perigee fixed. Extremely low thrust levels are found over most of the lifetime while increases in lifetime on the order of 30% over the nonthrusting case result. The second case considers thrusting at a constant level over a symmetrical arc about perigee; the length of the arc for each cycle being determined by the condition that the perigee remain fixed. Greatly increased lifetimes over the nonthrusting case and the preceding case are obtained with low mass consumption and small thrust-to-drag ratios. Expressions for the forces required to provide a secular change of the line of nodes, the line of apsides, and the inclination including the effect of planet oblateness are given and several examples are calculated.