We study the existence and stability of the relative equilibria of systems
of two satellites joined by a tether. Since tethers used in practice are ve
ry stiff we consider a stiff tether as a perturbation of an inextensible te
ther. We show that the equations for relative equilibria and the stability
conditions are continuous as stiffness approaches infinity and limit on the
equations and conditions relevant to an inextensible tether. We obtain a n
umerical bifurcation diagram for a class of relative equilibria in the case
of an inextensible tether.