The equations of motion for a class of Tethered Satellite Systems (TSS), undergoing planar motion in a Keplerian orbit, are derived. The system consists of a rigid platform from which a point mass subsatellite can be deployed or retrieved by a flexible tether. The model incorporates offset of the tether attachment point from the platform centre of mass and its time dependent variation. The governing equations of motion are obtained using the Lagrangian procedure. The effect of system parameters on the dynamics is analysed numerically. A hybrid strategy using thruster and offset control is used to regulate the tether swing. The platform dynamics are controlled by momentum gyros. It is shown that the control of only rigid degrees of freedom is not sufficient as the flexible dynamics of the tether becomes unstable, particularly during retrieval. Passive dampers are proposed to control the flexible dynamics. Effectiveness of the control strategy is assessed through its application to several cases of practical importance.