The present invention relates to a process for the production of polyunsaturated fatty acids in transgenic plants, by introducing, into the plant, the nucleic acids which code for polypeptides with .DELTA.6-desaturase, .DELTA.6-elongase, a .DELTA.5-desaturase, .DELTA.5-elongase, .DELTA.4-desaturase, .DELTA.12-desaturase and/or .omega.3-desaturase activity. These desaturases and elongases are advantageously derived from Phytophthora sojae. The invention furthermore relates to the nucleic acid sequences, nucleic acid constructs, vectors and organisms comprising the nucleic acid sequences according to the invention, vectors comprising the nucleic acid sequences and/or the nucleic acid constructs and to transgenic plants comprise the abovementioned nucleic acid sequences, nucleic acid constructs and/or vectors. A further part of the invention relates to fatty acid compositions produced by the process according to the invention and to their use.