The present invention provides bispecific antibody constructs of a specific Fc modality characterized by comprising a first domain binding to a target cell surface antigen, a second domain binding to an extracellular epitope of the human and/or the Macaca CD3cε chain and a third domain, which is the specific Fc modality. Moreover, the invention provides a polynucleotide, encoding the antibody construct, a vector comprising this polynucleotide, host cells, expressing the construct and a pharmaceutical composition comprising the same.