The present invention relates to genetic engineering and especially to the use of DNA transposition complex of bacteriophage Mu. In particular, the invention provides a gene transfer system for eukaryotic cells, wherein in vitro assembled Mu transposition complexes are introduced into a target cell and subsequently transposition into a cellular nucleic acid occurs. The invention further provides a kit for producing insertional mutations into the genomes of eukaryotic cells. The kit can be used, e.g., to generate insertional mutant libraries.