Mechanical stresses of the membrane of a fuel cell can be reduced by virtue of the fact that the supply of feed gas to a gas chamber of the fuel cell takes places, initially, by means of a first pressure increasing speed and then by means of a second pressure increasing speed. The first pressure increasing speed is slower than the second pressure increasing speed. Pressure surges are prevented in the membrane due to the lower pressure increasing speed in the first phase of the gas supply, and as a result, the life span of the membrane is increased.