Issues of stability of the Tethered Satellite System (TSS) during station-keeping, deployment and retrieval are considered. The basic nonlinear equations of motion of the TSS are derived using the system Lagrangian. Using the Hopf bifurcation theorem, tension control laws are established which guarantee the stability of the system during the station-keeping mode. A constant angle control method is hypothesized for subsatellite deployment and retrieval. It is proved that this control law results in stable deployment but unstable retrieval. An enhanced control law for deployment is also proposed, which entails use of the constant angle method followed by a station-keeping control law once the tether length is sufficiently near the desired value. Simulations are given to illustrate the conclusions.