A dual specificity polypeptide molecule comprising a first polypeptide chain and a second polypeptide chain, wherein: a) the first polypeptide chain comprises ai) a first variable domain (VD1) of an antibody, aii) a first variable domain (VR1) of a T cell receptor (TCR), and aiii) a first linker (LINK1) connecting said domains; b) the second polypeptide chain comprises bi) a second variable domain (VR2) of a TCR, bii) a second variable domain (VD2) of an antibody, and biii) a second linker (LINK2) connecting said domains; wherein said first variable domain (VD1) and said second variable domain (VD2) associate to form a first binding site (VD1)(VD2) that specifically binds a cell surface antigen of a human immune effector cell; wherein the first variable domain (VR1) is one of a TCR Vα domain and a TCR Vβ domain, and the second variable domain (VR2) is the other one of the TCR Vα domain and the TCR Vβ domain, said first variable domain (VR1) and said second variable domain (VR2) associate to form a second binding site (VR1)(VR2) that binds an MHC-associated viral peptide epitope; wherein said two polypeptide chains are fused to human IgG hinge domains and/or human IgG Fc domains or dimerizing portions thereof; wherein the said two polypeptide chains are connected by covalent and/or noncovalent bonds between said hinge domains and/or Fc-domains; wherein said dual specificity polypeptide molecule is capable of simultaneously binding the cell surface molecule and the MHC-associated viral peptide epitope; and wherein the order of the variable domains in the two polypeptide chains is selected from VD1-VR1 and VR2-VD2 or VD2-VR2 and VR1-VD1. a) the first polypeptide chain comprises ai) a first variable domain (VD1) of an antibody, aii) a first variable domain (VR1) of a T cell receptor (TCR), and aiii) a first linker (LINK1) connecting said domains; ai) a first variable domain (VD1) of an antibody, aii) a first variable domain (VR1) of a T cell receptor (TCR), and aiii) a first linker (LINK1) connecting said domains; b) the second polypeptide chain comprises bi) a second variable domain (VR2) of a TCR, bii) a second variable domain (VD2) of an antibody, and biii) a second linker (LINK2) connecting said domains; wherein said first variable domain (VD1) and said second variable domain (VD2) associate to form a first binding site (VD1)(VD2) that specifically binds a cell surface antigen of a human immune effector cell; wherein the first variable domain (VR1) is one of a TCR Vα domain and a TCR Vβ domain, and the second variable domain (VR2) is the other one of the TCR Vα domain and the TCR Vβ domain, said first variable domain (VR1) and said second variable domain (VR2) associate to form a second binding site (VR1)(VR2) that binds an MHC-associated viral peptide epitope; wherein said two polypeptide chains are fused to human IgG hinge domains and/or human IgG Fc domains or dimerizing portions thereof; wherein the said two polypeptide chains are connected by covalent and/or noncovalent bonds between said hinge domains and/or Fc-domains; wherein said dual specificity polypeptide molecule is capable of simultaneously binding the cell surface molecule and the MHC-associated viral peptide epitope; and wherein the order of the variable domains in the two polypeptide chains is selected from VD1-VR1 and VR2-VD2 or VD2-VR2 and VR1-VD1. bi) a second variable domain (VR2) of a TCR, bii) a second variable domain (VD2) of an antibody, and biii) a second linker (LINK2) connecting said domains; <EOS>