The invention relates to a method for carrying out the expansion of multipotent stem cells ex vivo. Moreover, the invention relates to a two-stage method for carrying out the expansion and differentiation of multipotent stem cells ex vivo, in which it is possible for the stem cells to be gene transfected during the first stage, i.e. during the expansion phase. In this phase, the differentiation of the multipotent stem cells takes place optionally in cells of the hematopoietic, endothelial or mesenchymal cell lineage. Stem and progenitor cells as well as mature cells of the hematopoietic, endothelial and mesenchymal cell lineage, which are obtained in this way, can be used, among other things, for the prophylaxis, diagnosis and therapy of human deseases and for tissue engineering.