The present invention relates to polynucleotides from Ostreococcus lucimarinus which code for desaturases and elongases and which can be employed for the recombinant production of polyunsaturated fatty acids. The invention furthermore relates to vectors, host cells and transgenic nonhuman organisms which comprise the polynucleotides, and to the polypeptides encoded by the polynucleotides. Finally, the invention also relates to production processes for the polyunsaturated fatty acids and for oil, lipid and fatty acid compositions.