The invention relates to a method for producing eicosapentanoic acid, docosapentanoic acid and/or docohexanoic acid in transgenic plants. According to said method, the plant is provided with at least one nucleic acid sequence coding for a polypeptide with a Δ6 desaturase activity, at least one nucleic acid sequence coding for a polypeptide with a Δ6 elongase activity, at least one nucleic acid sequence coding for a polypeptide with a Δ5 desaturase activity, and at least one nucleic acid sequence coding for a polypeptide with a Δ5 elongase activity, the nucleic acid sequence coding for a polypeptide with a Δ5 elongase activity being modified in relation to the nucleic acid sequence in the organism from which the sequence originates, such that it is adapted to the codon use in at least one type of plant. For the production of docosahexanoic acid, at least one nucleic acid sequence coding for a polypeptide with a Δ4 desaturase activity is also introduced into the plant.