The present invention concerns therapeutic agents that antagonize the activity of glucagon. In accordance with the present invention, the compounds of the invention comprise: a. a glucagon antagonist domain, preferably the amino acid sequence of SEQ ID NO: 7, or sequences derived therefrom by phage display, RNA-peptide screening, or the other techniques; and b. a vehicle, such as a polymer (e.g., PEG or dextran) or an Fc domain, which is preferred; wherein the vehicle is covalently attached to the glucagon antagonist domain. The vehicle and the glucagon antagonist domain may be linked through the N- or C-terminus of the glucagon antagonist domain. The preferred vehicle is an Fc domain, and the preferred Fc domain is an IgG Fc domain.