According to the legends, the forefather of the genus was Súr, a commander in the Battle of Lechfeld, son of Grand Prince Fajsz, thus a member of the Árpád dynasty.

Duke Beled, as told in the Chronicon Pictum, was the one who arranged the marriage between the Grand Prince Géza and Sárolt of Transylvania.

The eponymous ancestor of the clan was Osli I, descendant of Beled and of duke Kolán's daughter, who lived around between 1200 and 1230.

However, he had no male successors, thus the property were inherited by Lőrinc, Ispán of Zala County, his brother's sons.

After the Battle of Mohi (1241), he put in safety Béla IV and the royal family at Klis Fortress (Hungarian: Klissza) who fled from the Mongols to Dalmatia.