In Heavy Marine Transport it is common practice to drytransport large and heavy floating offshore structures. In general, loading and discharge of these floating cargoes on- and from heavy transport vessels is done at sheltered locations like harbors where sea-state and swell conditions are insignificant. Often these locations are at large distance from operating fields of the offshore structures, which means that the structures need to be towed from- or to these fields. To save time and costs, it is beneficial to perform the loading and discharge operations in the field. This necessitates a reconsideration of the maximum allowable wave condition such as to perform the loading- and discharge operations within specified time frame whilst ensuring safety of crew, cargo and heavy transport vessel. Since precise positioning of the cargo on the HTV cribbing beams is of importance to support the cargo on its structural strong points, the allowed relative horizontal motion during loading or discharge operations is limited to a fraction of the width of these cribbing beams. When increasing the maximum allowable wave conditions, relative horizontal motions between heavy transport vessel and cargo easily exceed these limits if only the standard handling equipment is used. Also, the loads in the handling equipment may exceed safe limits. This paper presents two methods including complementary equipment to reduce- and limit the relative horizontal motions. The first method is based on increasing the stiffness of the con-nection between cargo and heavy transport vessel. This means that there is a transition from a soft (standard handling) system with a low natural frequency to a stiff (clamping) system with high natural frequency. During this transition the system natural frequency will coincide with the wave frequent excitation force. Resonant behavior during the transition is avoided as the complementary equipment also employs a damping force. The second method is based on a closed-loop controller applied to the desired relative horizontal position. The resulting desired load to control the relative horizontal motion is then allocated to several line tension actuators. Contradictory to well-known Dynamic Positioning systems which control low frequent motions, motion control during offshore loading and discharge is performed on wave frequent behavior. This implies that the line tension actuators also need to deliver loads within a wave frequent time-frame. In fact, the peak tension needs to be obtained within a quarter of a wave period. System design and simulation results are presented. Depending on the cargo type, different solutions and operational aspects are discussed. Simulations are done for a typical cargo where both methods to reduce the relative horizontal motions are utilized.