Mesenchymal stromal cells (MSCs) are increasingly used in human cell therapy protocols. Two major issues, however, have yet to be addressed with this intriguing cell population: the likelihood of true transdifferentiation and isolation of MSC stem cells. To date, neither has been convincingly demonstrated. We have attempted to address both issues here. The demonstration of self‐renewal and differentiation ‐ key criteria for stem cell characteristics ‐ have yet to be accomplished. To address this issue, we rigorously generated true clones from the highly proliferative population of MSCs derived from non‐transformed human umbilical cord perivascular cells (HUCPVCs) that share the properties and immunophenotype of bone marrow‐derived MSCs. We demonstrated a hierarchy of differentiation potential along adipocytic, osteogenic, chondrogenic, myogenic and fibroblastic lineages. Future studies will be aimed at characterizing clones for the regeneration of specific tissues.To address the issue of transdifferentiation, we employed a novel in vitro system in which embryonic rat cardiomyocytes are co‐cultured with adult murine MSCs derived from transgenic animals carrying the cardiac‐specific myosin heavy chain promoter driving green fluorescence protein (GFP). We found that some cells expressed GFP and, additionally, had acquired several cardiac‐specific markers but nevertheless had retained all previously assayed MSC determinants, suggesting the generation of a unique cell population that we also showed had not arisen from cell fusion. Furthermore, electrophysiological studies revealed that these unique GFP+ cells do not generate action potentials or ionic currents typical of cardiomyocytes, indicating that the cells are functionally, stromal and not cardiomyocytes. The presence of this population in vivo was confirmed in studies with a murine experimental acute myocardial infarction model. The implications of these findings on the nature of tissue regeneration with exogenous MSCs will be discussed in detail.