Non-organic substances are separated from household garbage and the organic substances are fed in proportioned manner into a mixing tank (5) and converted into slurry by adding liquid. The slurry is crushed for homogenization purposes in a crushing means (10, 11) and passed into a closed holding container (13). It is then fed over a heat exchanger (15) and heated to 55.degree. to 60.degree. C. The slurry passes into a plurality of reaction vessels (16) in which the methane gas and carbon dioxide are produced. In a separating plant (22), the mixture of gaseous products is broken down into its components and some of the methane gas is recycled by bubbling it through both the holding tank and the reaction tank, the remainder being stored in gasholders (23). The organic substances are degraded much more rapidly through increasing the degradation temperature and as a result constructional expenditure can be reduced.