Abstract: The invention relates to a method for the fractioned separation of valuable substances from aqueous many-component mixtures such as aqueous wastes, sludges and sewage sludge under supercritical conditions. The invention also comprises valuable substance fractions that are enriched after the method according to the invention, more particularly phosphorous-containing and phosphorous- and ammonium-containing compounds such as fertilisers and synthesis gas as an energy source and as a valuable substance for the chemicals industry. The invention comprises devices for carrying out the methods. With the method and devices according to the invention, valuable substances can be completely recovered from wastes, sludges and sewage sludge and given a new use. The methods and devices are particularly suitable for recovering phosphorous and ammonium in the form of plant-available fertiliser, for recovering metals and heavy metals, for producing synthesis gas and for obtaining hydrogen from synthesis gas, i.e.