The invention describes a method and the relevant devices for permitting an operation stable with time of a stack of membrane fuel cells fed with air and a gas containing hydrogen and at least 100 ppm of carbon monoxide, characterised in that it provides for an oxidising condition at the anodes of said cells in a self-adjusting continuous way or sequentially discontinuous way. Different embodiments of the invention are illustrated wherein the oxidising condition is obtained by adding to the gas containing hydrogen and carbon monoxide, oxygen produced in an electrolysis cell integrated to the fuel cell stack, or by flowing air through porous areas obtained in the bipolar plates or by resorting to high gas diffusion rate membranes, wherein the air flow rate is regulated in both cases by adjusting the pressure differential existing between air and the gas containing hydrogen and carbon monoxide. According to a further embodiment of the method of the invention, the oxidising condition is obtained by sequentially short-circuiting the fuel cell stacks provided with external contacts connected to a control unit.