This invention relates to a new elongase gene having the sequence SEQ ID NO: 1 or its derivatives, to a gene construct comprising this sequence or its derivatives and to its use. The inventive nucleic acid sequence encodes a polypeptide which elongates .alpha.-linolenic acid (C.sub.18:3 d9, 12, 15) by at least two carbon atoms whereas .gamma.-linolenic acid (C.sub.18:3 d6, 9, 12) is not elongated. The invention additionally relates to vectors or organisms comprising an elongase gene having the sequence SEQ ID NO: 1 or its derivatives.The invention further relates to a process for the production of polyunsaturated fatty acids (=PUFAs) with an organism which comprises the elongase gene and which organism produces high amounts of oils and especially oils with a high content of unsaturated fatty acids. Additionally the invention relates to an oil and/or fatty acid composition with a higher content of polyunsaturated C.sub.20 or C.sub.22 fatty acids with at least two double bonds and/or to a triacylglycerol composition with a higher content of said polyunsaturated fatty acids.