Methods for inducing a population of T cells to proliferate by activating the population of T cells and stimulating an accessory molecule on the surface of the T cells with a ligand which binds the accessory molecule are described. T cell proliferation occurs in the absence of exogenous growth factors or accessory cells. T cell activation is accomplished by stimulating the T cell receptor (TCR)/CD3 complex or the CD2 surface protein. To induce proliferation of an activated population T cells, an accessory molecule on the surface of the T cells, such as CD28, is stimulated with a ligand which binds the accessory molecule. The T cell population expanded by the method of the invention can be genetically transduced and used for immunotherapy or can be used in methods of diagnosis.