The invention relates to nucleic acid(s) which is/are obtained from tetrahymena and which code(s) for a ciliate-specific delta-6-desaturase that is involved in the biosynthesis of commercially valuable, multiply unsaturated fatty acids (so-called PUFA) polyunsaturated fatty acids). The inventive nucleotide sequence and the polypeptide sequence that can be obtained therefrom exhibit a surprisingly low sequence identity compared to other known natural desaturases. The invention also relates to the use of the nucleic acid(s) for overexpression in ciliates, preferably tetrahymena, in particular, Tetrahymena thermophila, with the aim of increasing the production of delta-6 unsaturated fatty acids, especially GLA.