The invention relates to a method for producing polyunsaturated fatty acids in an organism, according to which nucleic acids coding for polypeptides with an acyl-CoA:lysophospholipid-acyltransferase activity are introduced into the organism. Advantageously, the nucleic acid sequences can be expressed in the transgenic organism optionally together with other nucleic acid sequences coding for polypeptides of the fatty acid or lipid metabolism. The invention also relates to the inventive nucleic acid sequences, nucleic acid constructs containing the inventive nucleic acid sequences, vectors containing the inventive nucleic acid sequences and/or the nucleic acid constructs, and transgenic organisms containing the nucleic acid sequences, nucleic acid constructs and/or vectors. The invention further relates to oils, lipids and/or fatty acids produced according to the inventive method, and to the use of the same.