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