Disclosed are two PTH analog ligands, SP-PTH-AAK and Aib-SP-PTH-AAK, that have long-acting activity at the PTH receptor, as demonstrated both in vitro and in vivo. These polypeptides are thus particularly useful in the treatment of diseases, such as hypoparathyroidism, in which long-acting activity is desired. The method of making the analog polypeptides is also disclosed.