A tether management system of a winch module in a marine environment is proposed. For the purpose of this study the subsea body is considered as a mass attached at the free end of a long tether which is wrapped around a circular drum controlled by an external torque. The winch is considered mounted on a heaving platform. The effect of the heaving platform on the motions of the drum, tether and attached mass are studied with respect to the longitudinal vibrations of the tether in one dimension. The resulting nonlinear system of equations of motion is developed and solved numerically for an example of a marine tether system.