A first bispecific antibody molecule comprises at least one binding site with a variable domain on a light chain (V.sub.L) and a variable domain for the T-cell receptor CD-28, linked thereto on a heavy chain (V.sub.h). The antibody molecule further comprises at least one binding site with a variable domain on a heavy chain (V.sub.H) and a variable domain for a tumour antigen, linked thereto on a light chain (V.sub.L). The variable domains on the heavy chains for both specificities are connected to each other by means of a peptide linker. A second bispecific antibody molecule is bivalent for CD-28 and at least monovalent for the tumour antigen.