A process for increasing the concentration of PUFA triglycerides present in natural PUFA oils, in which a natural PUFA oil having a triglyceride content of more than 85% by weight, based on the total weight of the mixture, and having a total PUFA content of more than 39% by weight of total fatty acids is dissolved in an organic solvent or an organic solvent mixture, the mixture is allowed to stand at a temperature of from -35.degree. C. to -100.degree. C. for a period of more than five minutes, the mixture is separated into a supernatant comprising PUFA-triglyceride mixture and a sediment phase, the separation preferably taking place by filtration or centrifugation, and the solvent or solvent mixture, after the removal of the sediment phase, is separated from the supernatant. PUFA-triglyceride mixtures having a PUFA content of more than 55% by weight of total fatty acids of a main PUFA, or at least two PUFAs selected from stearidonic acid, eicosapentaenoic acid, docosapentaenoic acid, docosahexaenoic acid, gamma-linolenic acid and arachidonic acid, and also use thereof in pharmaceutical, cosmetics and food preparations.