Provided herein are monovalent antigen-binding constructs targeting EGFR and/or HER2. The monovalent antigen-binding constructs can include at least one antigen-binding polypeptide comprising a heavy chain variable domain, wherein the antigen-bind polypeptide specifically binds EGFR and/or HER2; and a heterodimeric Fc domain, the Fc domain comprising at least two CH3 domains, wherein the Fc domain is coupled, with or without a linker, to the antigen-binding polypeptide. Also provided are methods of making the constructs and methods of using the constructs.