The present invention refers to hyperactive variants of a transposase of the transposon system Sleeping Beauty (SB). The invention further refers to corresponding nucleic acids producing these variants, to a gene transfer system for stably introducing nucleic acid(s) into the DNA of a cell by using these hyperactive variants of a transposase of the transposon system Sleeping Beauty (SB) and to transposons used in the inventive gene transfer system, comprising a nucleic acid sequence with flanking repeats (IRs and/or RSDs). Furthermore, applications of these transposase variants, the transpsoson, or the gene transfer system are also disclosed such as gene therapy, insertional mutagenesis, gene discovery (including genome mapping), mobilization of genes, library screening, or functional analysis of genomes in vivo and in vitro. Finally, pharmaceutical compositions and kits are also encompassed.