The process and the apparatus serve for separating a gas mixture in a separation plant. A feed gas (18) is introduced into a compressor system (6, 16) and then into the separation plant. In the event of loss or partial loss of the compressor system (6, 16) of the first feed gas compressor (6), a first auxiliary stream (91, 92) which has approximately the composition of the first product stream or approximately the composition of the feed gas is compressed (78, 89) to at least approximately the first pressure and is recirculated to the separation plant.