A method for the high-temperature electrolysis of steam H 2 O, or for the co-electrolysis of steam H 2 O and of carbon dioxide CO 2, implemented in a reactor comprising a stack of individual electrolysis cells (C1, C2) of solid oxide type, each formed of a cathode (2.1, 2.2), of an anode (4.1, 4.2) and of an electrolyte (3.1, 3.2) inserted between the cathode and the anode, and a plurality of electrical and fluid interconnectors (5.1; 5.2) each arranged between two adjacent individual cells (C1, C2) with one face thereof in electrical contact with the anode (4.1) of one of the two individual cells and the other face thereof in electrical contact with the cathode (2.2) of the other of the two individual cells, according to which: - a first zone (61, 71, 81) of each interconnector (5.1) of a first group is supplied with steam (EH2) or with a mixture of steam H 2 O and of carbon dioxide CO 2, and it is distributed to a cathode of each individual cell of the first group, then the hydrogen H 2 produced (SH2) or the synthesis gas (mixture of carbon monoxide CO and of hydrogen H 2) is recovered in a second zone (63, 73, 83) of each interconnector of the first group, - a first zone (62, 73, 82) of each interconnector (5.2) of a second group, at least one of which is adjacent to an interconnector of the first group, is supplied with steam (EH2) or with a mixture of steam H 2 O and of carbon dioxide CO 2, and it is distributed to a cathode of each individual cell of the second group, at least one of which is adjacent to a cell of the first group, then the hydrogen H 2 produced (SH2) or the synthesis gas (mixture of carbon monoxide CO and of hydrogen H 2) is recovered in a second zone (64, 71, 84) of each interconnector of the second group, the first and second zones of the interconnectors (5.2) of the second group not being located vertically in line respectively with the first and second zones of the interconnectors (5.1) of the first group, according to which method, within the stack, the supply and the circulation respectively to the interconnectors and to the cells of the first group are carried out independently relative to the supply and circulation respectively to the interconnectors and to the cells of the second group. - a first zone (61, 71, 81) of each interconnector (5.1) of a first group is supplied with steam (EH2) or with a mixture of steam H 2 O and of carbon dioxide CO 2, and it is distributed to a cathode of each individual cell of the first group, then the hydrogen H 2 produced (SH2) or the synthesis gas (mixture of carbon monoxide CO and of hydrogen H 2) is recovered in a second zone (63, 73, 83) of each interconnector of the first group, - a first zone (62, 73, 82) of each interconnector (5.2) of a second group, at least one of which is adjacent to an interconnector of the first group, is supplied with steam (EH2) or with a mixture of steam H 2 O and of carbon dioxide CO 2, and it is distributed to a cathode of each individual cell of the second group, at least one of which is adjacent to a cell of the first group, then the hydrogen H 2 produced (SH2) or the synthesis gas (mixture of carbon monoxide CO and of hydrogen H 2) is recovered in a second zone (64, 71, 84) of each interconnector of the second group, the first and second zones of the interconnectors (5.2) of the second group not being located vertically in line respectively with the first and second zones of the interconnectors (5.1) of the first group,