Connection system for passage between floating bodies, comprising: - a bridge structure for passage between a first floating body and a second floating body; - a first coupling between the bridge structure and the first floating body; and - a second coupling between the bridge structure and the second floating body; the system is characterized in that: the first coupling comprises a first active trimmer and a first support for the bridge structure connected to a first supporting platform; the second coupling comprises a second active trimmer and a second support for the bridge structure connected to a second supporting platform; wherein both active trimmers (5, 9) are configured to stabilize the supporting platforms (4, 8) by trimming movements of floating bodies (2, 6) to maintain a required position of the bridge structure, said both active trimmers (5, 9) comprising a position and orientation sensors, a data control and processing means and an active trimmer actuation means, wherein the position and orientation sensors are configured to determine a position and/or orientation of the floating bodies (2, 6) and/or the bridge structure to stabilize the bridge structure in the required position; wherein the data control and processing means are configured to process the position and/or orientation of the floating bodies and/or the bridge structure and for control the active trimmer actuation means to generate a resulting trim movement in the supporting platforms (4, 8); and wherein the active trimmer actuation means are configured to move the supporting platforms (4, 8) to the required stabilizing position and stay in said position. - a bridge structure for passage between a first floating body and a second floating body; - a first coupling between the bridge structure and the first floating body; and - a second coupling between the bridge structure and the second floating body; the first coupling comprises a first active trimmer and a first support for the bridge structure connected to a first supporting platform; the second coupling comprises a second active trimmer and a second support for the bridge structure connected to a second supporting platform; wherein both active trimmers (5, 9) are configured to stabilize the supporting platforms (4, 8) by trimming movements of floating bodies (2, 6) to maintain a required position of the bridge structure, said both active trimmers (5, 9) comprising a position and orientation sensors, a data control and processing means and an active trimmer actuation means, wherein the position and orientation sensors are configured to determine a position and/or orientation of the floating bodies (2, 6) and/or the bridge structure to stabilize the bridge structure in the required position; wherein the data control and processing means are configured to process the position and/or orientation of the floating bodies and/or the bridge structure and for control the active trimmer actuation means to generate a resulting trim movement in the supporting platforms (4, 8); and wherein the active trimmer actuation means are configured to move the supporting platforms (4, 8) to the required stabilizing position and stay in said position.