(57) To avoid environmental objections in discarding by-products of refining and processing pf fatty oils, fats or mineral oils, especially those containjng alkali metal ions or salts, such by-products are combpsted with excess air or oxygen, preferably in a fluidized bed oven, using a bed material having a low silicon content, particularly those consisting mainly of titanium, calcium and/or aluminium oxides, at 600-950°C, preferably 800-850°C. The organic materials in the by-products are thereby converted into products which can be discharged without problems; the exhaust gases contain only low amounts of carbon monoxide and nitrogen oxides. By passing the combustion gases through a heat-exchanger, the heat generated can be used, e.g. to preheat the excess air for the process or to generate steam or heated water, which can be used economically in other parts of the plant. The process is particularly suitable for the combustion of soapstock, the water content of which has been reduced, e.g. by evaporation, if necessary.