The invention relates to a process for the production of long-chain polyunsaturated fatty acids in an organism by introducing, into the organism, nucleic acids coding for polypeptides with acyltransferase activity. These nucleic acid sequences, if appropriate together with further nucleic acid sequences coding for polypeptides of the fatty acid or lipid metabolism biosynthesis, can advantageously be expressed in the organism. Furthermore, the invention relates to a method for the production of oils and/or triacylglycerides with an elevated content of long-chain polyunsaturated fatty acids. The invention furthermore relates to the nucleic acid sequences, and constructs, vectors and organisms comprising the nucleic acid sequences. A further part of the invention relates to oils, lipids and/or fatty acids produced by the process according to the invention and to their use.