The invention relates to a method for the production of multiply-unsaturatedfatty acids in an organism, into whichnucleic acids have been introduced, which code for polypeptides with .DELTA. -5 elongase activity. Said nucleic acid sequences, optionallywith further nucleic acid sequences, coding for polypeptides for thebiosynthesis of fatty acids and lipid metabolism, are advantageouslyexpressed in the organism. Nucleic acid sequences coding for a .DELTA. -6desaturase, a .DELTA.-5 desaturase, .DELTA. -4 desaturase and/or.DELTA.-6 elongase activity are particularly advantageous and, advantageously,said saturases and elongases are derived from Thalassiosira,Euglena or Ostreococcus. The invention further relates to a method for theproduction of oils and/or triacylglycerides withan increased content of long-chain, multiply-unsaturated fatty acids. Aparticular embodiment of the invention is a method for theproduction of unsaturated co-3 fatty acids and a method for the production oftriglycerides with an increased content of unsaturatedfatty acids, in particular, of .DELTA.-3 fatty acids with more than threedouble bonds. Also disclosed is the production of a transgenicorganism, preferably a transgenic plant, or a transgenic microorganism withincreased content of .omega.-3 fatty acids, oils or lipids with .omega.-3double bonds as a result of the expression of the elongases and desaturasesemployed in the above method, preferably in combinationwith .omega.-3 desaturases, for example a .omega.-3 desaturase from fungi ofthe family Pythiaceae such as the genus Phytophtora, for example,the genus and species Phytophtora infestans, or a .omega.-3 desaturase fromalgae such as the family Prasinophyceae, for example, thegenus Ostreococcus and, particularly, the genus and species Ostreococcus taurior diatomacew such as the genus Thalassiosira and,particularly, the genus and species Thalassiosira pseudonana. The inventionalso r
