The invention relates to a method for cracking hydrocarbons, especially for producing olefins, whereby a mixture consisting of hydrocarbons and water vapor is heated in a cracking furnace up to a temperature ranging from 750 °C to 900 °C, and the resulting cracking gas which contains hydrogen is immediately cooled after the heating process in a cracking gas cooler to a temperature lower than approximately 650 °C. If heavy products are present, the cracking gas is subsequently subjected to an additional cooling by quenching and is then liberated by separating out heavy oil and gasoline. Afterwards, water vapor is removed by quenching from the cracking gas containing light products. This cracking gas is compressed to at least 20 bar by a compressor, is liberated from residual water by drying, is cooled in a deep cooling installation, and is fed into a plurality of rectifying columns in order to separate out the light products. Selective membrane diffusion is used to extract a portion of the hydrogen from the cracking gas in the direction of flow of the process medium upstream from the deep cooling installation. The invention also relates to an installation for thermally cracking hydrocarbons, especially for producing olefins.