An apparatus for chlor-alkali electrolysis, comprising a cathode half-cell, an oxygen-consuming electrode arranged therein, a conduit for supply of gaseous oxygen to the cathode half-cell and a conduit for purging the cathode half-cell with inert gas, enables the flexible use of power by a method in which chlorine is produced in the apparatus by chlor-alkali electrolysis, wherein, when power supply is low, the oxygen-consuming electrode is supplied with gaseous oxygen, and oxygen is reduced at the oxygen-consuming electrode at a first cell voltage, and when power supply is high, the oxygen-consuming electrode is not supplied with any oxygen, and hydrogen is generated at the cathode at a second cell voltage which is higher than the first cell voltage.