The invention relates to a method for producing arachidonic acid and/or eicosapentaenoic acid in useful transgenic plants, according to which nucleic acids, which encode polypeptides with .DELTA.-6-desaturase activity, .DELTA.-6-elongase activity or .DELTA.-5-desaturase activity, are introduced into the plants. As an added advantage, a gene that encodes a .DELTA.-3-desaturase is expressed in the useful plants. In an additional embodiment of the method, additional nucleic acid sequences, which encode polypeptides involved in the biosynthesis of the fatty acid or lipid metabolism, can be expressed in the plants. Particularly advantageous nucleic acid sequences are those that encode .DELTA.-8-desaturase activity, .DELTA.-12-desaturase activity, .DELTA.-15-desaturase activity, .DELTA.-4-desaturase activity, .DELTA.-9-elongase activity and/or .DELTA.-5-elongase activity. The invention also relates to the use of the oils, lipids and/or fatty acids that have been produced by said method in animal feed or foodstuffs, cosmetics or pharmaceutical products.
