A mixture containing fatty acid glycerides which has a high percentage content of PUFA acyl groups and a low percentage content of saturated fatty acid acyl groups is described. A process which enables the PUFA acyl groups in a mixture containing fatty acid glycerides (for example a fish oil) to be enriched and, at the same time, the content of saturated fatty acid acyl groups to be maintained at a low content is described. The process is a hydrolytic process or an alcoholysis in which the fatty acid acyl groups to be enriched are hydrolytically or alcoholytically released from the fatty acid glycerides slowly, if at all, the process being carried out in the presence of a lipase.