A condensate suction pipe rotating with the drying cylinder extends from the area of the axis of rotation of the drying cylinder toward the inside surface of the cylinder shell, and has there a suction opening for the intake of condensate mixed with steam. A steam blowing line originating from the cylinder interior empties in the area of the suction opening into the interior of the condensate suction pipe. The steam blowing line is fashioned as an annular channel defined by the radially outer (relative to the cylinder axis) area of the condensate suction pipe and by an outside pipe surrounding the condensate suction pipe.