The Habsburgs did eventually gain descent from the Babenberg dukes, though at different times. The first Habsburg line to be descended from the Babenbergs was the Albertine line. This was achieved through the marriage of Albert III, Duke of Austria to Beatrix of Nuremberg. As such, their son, Albert IV, Duke of Austria, was the first Habsburg duke who was descended from the Babenberg dukes. However, the male line of that branch of the Habsburgs died out in 1457 with Ladislas V Posthumus of Bohemia.
The Habsburgs did eventually gain descent from the Babenberg dukes though at different times. The first Habsburg line to be descended from the Babenbergs was the Albertine line. This was achieved through the marriage of Albert III, Duke of Austria to Beatrix of Nuremberg. As such, their son Albert IV, Duke of Austria, was the first Habsburg duke who was descended from the Babenberg dukes. However the male line of that branch of the Habsburgs died out in 1457 with Ladislas V Posthumus of Bohemia.