Progenitor cells that seed the fetal thymus are derived from the fetal liver and the bone marrow. These cells migrate through the fetal blood to the thymus. In this work, we address which peripheral progenitor cells have the potential to become T cells and whether these progenitor cells are already committed to the T cell lineage. All CD34+CD38- precursor cells, regardless of their origin, are able to develop into T cells in a hybrid human/mouse fetal thymic organ culture. Previously, we found that the more differentiated CD34+CD38+ progenitor cells from fetal liver cannot develop into T cells. In this work, we show that CD34+CD38+ cells from fetal bone marrow and cord blood are capable of T cell development. In spite of the T cell-developing potential, we did not detect rearrangements of TCR-delta or TCR-beta loci in any of the CD34+ peripheral precursors. CD34+ fetal bone marrow cell subpopulations express pre-TCR-alpha. However, we could not detect expression of pT alpha or of recombination-activating gene 1 in CD34+ cord blood cells. Since cord blood CD34+ cells should contain the direct progenitors of the CD34+ thymocytes, our data do not support the notion that in humans commitment to the T cell lineage occurs before the cells migrate into the thymus.