RBITING space vehicles which use momentum exchange control elements such as control moment gyros (CMGs) and reaction wheels are faced with the problem of possible saturation of such devices. The use of gravity-gradi ent torques for desaturation control would allow the dissipation of accumulated momentum without expending vehicle propellants. This study is concerned with the momentum management problem as related to a cylindrical vehicle with the minimum momentum-of-inertia axis solar or stellar oriented. This particular configuration represents the most difficult class of vehicles for gravity-gradient desaturation. The regions of momentum control are compared for a reflexive maneuvering and a gravity tracking desaturation philosophy.