A stromal stem cell is obtained by isolation of a cell from a mixed population of mammalian cells based on expression of a cell surface marker, wherein the cell surface marker binds an antibody, wherein said antibody cross reacts with a cell surface marker found on a cell of at least one other mammalian species selected from human, mouse, rat, horse, rabbit and pig cells, and wherein the mixed population of cells comprises umbilical cord cells or umbilical cord blood cells.