Abstract: Several forms of immunoregulatory substances are derived from monoclonal antibodies (MAbs) that are specific for a T cell surface antigen, such as CD3, TCR, CD4, or CD8 on T cells. The substances include: a mixture of F(ab′)2 fragments (or other divalent binding molecules which lack Fc) which each bind noncompetitively to different monovalent antigenic epitopes on the same antigen; the F(ab′)2 fragment (or other divalent binding molecules which lack Fc) of a bispecific antibody which has each of its binding sites derived from one of the two MAbs that bind noncompetitively to monovalent antigenic epitopes on the same antigen; a conjugate including a polymeric backbone, such as polyethylene glycol (“PEG”), cellulose, dextran, agarose, or an amino acid copolymer or a liposome, that is coupled with the binding molecules, e.g., Fv, Fab, or F(ab′)2, which bind noncompetitively to monovalent antigenic epitopes on the same antigen.