The invention relates to an electrochemical battery, in particular a fuel cell battery or electrolytic cell battery comprising several electrolytic electrode units, a number of cooling cards for respectively cooling at least one of the electrolytic electrode units and at least one pressure chamber, which can be impinged by a pressure independently of the media supply of the electrolytic electrode units, for creating a contact pressure between components of the electrochemical battery that adjoin the pressure chamber. The pressure chamber adjoins at least one of the cooling cards and is at least partly delimited by said cooling cards.