The invention relates to a method and an apparatus for producing liquid-contents-filled containers (22) from preforms (1) by contents being introduced into the preform (1) under a filling pressure, wherein the contents are placed under pressure by a pressure pump (7) and are introduced into the preform (1) at a molding and filling station (3) by a filling valve (6). A pressure accumulator (10) arranged between the pressure pump (7) and the filling valve (6) is subjected to pressure and is filled with a volume of contents by the pressure pump (7). The invention is distinguished in that a displacement pump (26) having a filling chamber (28) for the contents and having a displacement body (30) guided so it is movable therein is provided, wherein the displacement body (30) divides the chamber (28) into a first partial chamber (28a) on the filling station side and a second partial chamber (28b) facing away from the filling station, each of which can be brought into a fluidic connection with the pressure accumulator (10). The displacement body (30) has a drive connection to a drive unit (32) and is drivable by the drive unit (32), wherein when the filling valve (6) is opened, the drive unit (32) and/or the pressure accumulator (10) each at least temporarily apply a drive force to the displacement body (30), and at the same time the displacement body (30) displaces at least a part of the quantity of contents required for the forming of the preform (1) in the direction of the preform (1).