Disclosed is an apparatus for the follow-up treatment, in particular cooling, of container products, which are produced by means of a blow-moulding, filling and closing process, and which can be fed to a follow-up treatment zone, which has an influencing effect, in particular a cooling effect, on the respective container product. The container products enter the follow-up treatment zone singly separate from one another or together in individual groups separate from one another comprising multiple container products. The follow up treatment zone is provided with at least one control means, acting on the container products and determining the time for which they stay in the follow-up treatment zone.