A system for use in petroleum production at sea includes a guide frame for one or more riser pipes, on a semisubmersible production vessel. One or more main buoyancy member are arranged separately on at least one riser to carry the main part of the riser's weight. Each riser separately carries a Christmas tree on its top, near a main deck of the vessel. The guide frame comprises vertical main elements extending vertically downwards from the deck, through the splash zone and through the upper, more wave- and current-influenced zone of the sea. The guide frame also includes horizontal guide plates comprising vertically open cells formed of a horizontally arranged framework of beams. Lateral stabilization devices guide the risers' and the main buoyancy members' vertical movement relative to the vessel and restrict horizontal movement of the risers with respect to the guide frame. The guide plates are arranged in at least two levels on the guide frame. A lower guide plate is arranged at the lower ends of the vertical main elements', and a guide plate is arranged just below or near the splash zone. At least one main buoyancy member is held on the riser in level with, and guided by, lateral stabilization devices arranged in one or more guide plates below the upper, more wave- and current-influenced zone near the sea surface. The risers are without buoyancy elements through the splash zone, and thus are less exposed to the water forces in the upper zone of the sea.