In this work, the controlled deployment and retrieval of tethered marine subsea systems are studied. The subsea body is here considered to be a mass attached at the free end of a long tether which is wrapped around a circular drum controlled by and external torque. The motion of the deployed and undeployed parts are examines and described. The hydrodynamic effects are considered on both the deployed portion of the tether and the tethered mass which are assumed submerged in otherwise still water, however the free surface effect is neglected together with the friction on the drum surface. The coupling effects between the drum, tether and attached mass are studied while the tether is deployed/retrieved/ The longitudinal elastic extension of the tether in one dimension is accounted for. Kane's formalism is used to write the relevant equations of motion which are expressed in matrix form, amenable for algorithm development. The resulting nonlinear system of ordinary differential equations are developed and solved numerically for an example of an almost neutrally buoyant marine tether system. The numerical results and their analysis for the retrieval and deployment of the system are presented.