A process for aerobic, fermentative hydrolysis, in particular for composting organic materials (1), is carried out in a closed container (5). Fresh air (7, 26) is fed into the organic materials (1). The warm moisture-laden outgoing air (8, 25) is conducted away. The customary presence of noxious substances, and in particular the unpleasant odours, is prevented by cooling the outgoing air to condense the moisture it contains (14). The dry outgoing air is then conveyed at ambient temperature to the atmosphere. A device for carrying out this process comprises a fermentation container (5) for receiving the organic materials (1) to be processed with a fresh air inlet and an outgoing air outlet for removal of the warm moisture-laden outgoing air. The presence of noxious substances, in particular the unpleasant odours in the atmosphere, is prevented by the use of a fermentation container (5) closed on all sides and by the provision of a heat-exchanger (9, 28) in which the heat in the outgoing air is absorbed by a heat-transfert medium, preferably the incoming fresh air, in order to condense (14) the moisture in the outgoing air.