A traction system (11; 60) for operating lines (18), in particular mooring lines and/or riser lines, of a vessel (1), includes at least two work stations (26) distributed along at least two sides of the vessel (1) and engaged by respective operating lines (18). The traction system includes a main traction device (14; 15, 17; 15A, 17) and a transmission device (36) having a duty line (28) connected to the main traction device and at least one guide member (24) for selectively routing the duty line (18) to each work station (26) for attachment to a respective operating line (18). A line storing space (22; 42, 44) is provided for storing parts of the duty line and/or hauled in moorings lines; the main traction device, the transmission device and the line storing space are placed together at or near a side of the floating production unit.