After deriving a set of dynamic equations governing the dynamics of a tethered satellite system (TSS), stabilizing tension control laws in feedback form are derived. The tether is assumed rigid and massless, and the equations of motion are derived using the system Lagrangian. It is observed that, to stabilize the system, tools from stability analysis of critical nonlinear systems must be applied. This paper employs tools related to the Hopf bifurcation theorem in the construction of the stabilizing control laws, which may be taken purely linear. Simulations illustrate the nature of the conclusions and show that nonlinear terms in the feedback can be used to significantly improve the transient response.