Transgenic non-human mammals that reproduce human pathologies of stem cell origins, such as chromosomal anomalies associated with chronic myeloid leukemia, B-cell acute lymphoblastic leukemia, T-cell acute or lymphoblastic leukemia, or with the migration of hematopoietic or embryonic stem cells. The transgenic non-human mammals can be produced using as a strategy the expression of genes involved in said pathologies by means of a promoter that directs the expression of a transgene in Sca-1.sup.+ cells. Said transgenic animals constitute a model for the study of said diseases and for the evaluation of compounds for the treatment and/or prevention of the diseases. Also disclosed are DNA construct and methods useful for producing the non-human transgenic mammals.