This paper is devoted to the nonlinear resonance of an in-plane tethered satellite system connected by an elastic tether. A planar dynamical model of the tethered satellite system that moves in an elliptical orbit during station-keeping phase is established using Kane’s equation method first. And then, the modulation equations are obtained based on the method of multiple scales, and the analytical solutions of which in terms of Jacobi elliptic function are given as well. Subsequently, the parameter conditions for periodic and non-periodic oscillations are analyzed through use of a graphical solution method. The results show that orbital eccentricity does not affect the resonance. Under resonant responses, the system energy would have an exchange between the two modes of oscillation; the period of mode amplitude would vary with the initial values of mode amplitudes. It is found that there exist the saturation phenomena for mode amplitude once the detuning parameter falls within a small region.