A method and device for producing containers filled with a liquid filling material from preforms made of a thermoplastic material, wherein the respective preform is at least thermally conditioned and subsequently re-formed during a forming and filling phase into the container with at least one liquid filling material as a pressure medium having a filling pressure p2. The filling material or portions of the filling material is/are supplied at at least two points in time and/or during at least two process phases having different carbon dioxide contents and/or different temperatures. The filling pressure p2 of the container formed in the first process phase is reduced to a pressure p1 and filling material is supplied in the second process phase, after which the pressure of the container is reduced to atmospheric pressure p0. In the first process phase filling material that has been previously degassed and/or uncarbonated is supplied.