The present invention relates to glucagon peptide agonists which have improved solubility and stability, to the use of the peptides in therapy, to methods of treatment comprising administration of the peptides to patients in need thereof, and to the use of the peptides in the manufacture of medicaments. The glucagon peptides of the invention are of particular interest in relation to the treatment of hypoglycemia, diabetes and obesity, as well as a variety of diseases or conditions associated with hypoglycemia, diabetes and obesity.