The present invention relates to glucagon receptor agonists and their medical use, for example in the treatment of severe hypoglycemia. Provided are exendin-4 analogues which potently and selectively activate the glucagon receptor and show a higher solubility at a near neutral pH and an enhanced chemical stability in solution compared to natural glucagon. The analogues have the artificial amino acid 4-Thiazolylalanine at position 1. This results in higher selectivity towards the glucagon receptor versus the GLP1 receptor when identical compounds are compared to each other differing only at position 1 (Tza in position 1 instead of His). The present invention provides highly selective glucagon receptor agonists.