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 Δ-12-/Δ-15-desaturase, Δ-9-elongase, Δ-8-desaturase and a Δ-5-desaturase and a process for the production of lipids or oils having an increased content of unsaturated fatty acids, in particular ω-3 and ω-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 Ciβ- or C20-fatty acids with a double bond in position Δ 5, 8, 9, 11, 12, 14, 15 or dffthe fatty acid produced, respectively due to the expression of the Δ-12-/Δ-15-desaturase, of the Δ-9-elongase, of the Δ-8-desaturase and of the Δ-5-desaturase in the plant. The expression of the inventive Δ-12-/Δ-15-desaturase leads preferably to linoleic acid and linolenic acid as products having a double bond in the position Δ 9, 12 and 15 of the fatty acid. The invention additionally relates to specific nucleic acid sequences encoding for proteins with Δ-12-/Δ-15-desaturase-, Δ-9-elongase-, Δ-8-desaturase- or Δ-5-desaturase-activity, nucleic acid constructs, vectors and transgenic plants containing said nucleic acid sequences.