A traction system for operating lines, in particular mooring lines and/or production lines, of a floating production unit has a number of work stations distributed along the unit, at least at two ends of the unit, and engaged by respective operating lines; a main winch; and a cable transmission device having a duty cable connected to the main winch, and guide means for selectively routing the duty cable to each work station for attachment to a respective operating line; at least one auxiliary winch, having an auxiliary cable connectable to the duty cable, is used to unwind the duty cable off the main winch and run the duty cable, along paths defined by the guide members, into a number of positions close to respective work stations.