Abstract: A process is proposed for the chemical oxidative treatment of a medium, e.g. sewage sludge, containing organic constituents, which comprises two process steps. In the first process step, the medium is heated to a first preset low temperature range and kept in this temperature range for a preset treatment duration. In a second process step, the sludge is then heated to a second preset low temperature range, pressurized in a preset low pressure range and kept in this temperature and pressure range for a preset treatment duration. In the course of this, an oxygen-containing gas, e.g. air or oxygen-enriched air or technical grade oxygen is introduced into the medium at least intermittently. The low temperatures and pressures provided in the two process steps are below or at most in the lower third of the temperature and pressure ranges of 150.degree.-370.degree. C. and 10-220 bar conventional in the wet-oxidation processes.