The present invention relates to a new process for the production of arachidonic acid and/or eicosapentaenoic acid in plants through the co-expression of a .DELTA.-12-/.DELTA.-15-desaturase, .DELTA.-9-elongase, .DELTA.-8-desaturase and a .DELTA.-5-desaturase and a process for the production of lipids or oils having an increased content of unsaturated fatty acids, in particular .omega.-3 and .omega.-6 fatty acids having at least two double bonds and a 18 or 20 carbon atom chain length. Preferably the arachidonic acid and eicosapentaenoic acid are produced in at least a 1:2 ratio. The invention furthermore relates to the production of a transgenic plants, preferably a transgenic crop plant, having an increased content of arachidonic acid and/or eicosapentaenoic acid, oils or lipids containing C.sub.8-- or C.sub.20-- fatty acids with a double bond in position 5, 8, 9, 11, 12, 14, 15 or 17 of the fatty acid produced, respectively due to the expression of the .DELTA.-12-/.DELTA.-15-desaturase, of the .DELTA.-9-elongase, of the .DELTA.-8-desaturase and of the .DELTA.-5-desaturase in the plant. The expression of the inventive .DELTA.-12-/.DELTA.-15-desaturase leads preferably to linoleic acid and linolenic acid as products having a double bond in the position 9, 12 and 15 of the fatty acid. The invention additionally relates to specific nucleic acid sequences encoding for proteins with .DELTA.-12-/.DELTA.-15-desaturase-, .DELTA.-9-elongase-, .DELTA.-8-desaturase- or .DELTA.-5-desaturase-activity, nucleic acid constructs, vectors and transgenic plants containing said nucleic acid sequences.