Cydippe was the mother of Cleobis and Biton.
Cydippe, a priestess of Hera, was on her way to a festival in the goddess' honor. The oxen which was to pull her cart were overdue and her sons, Biton and Cleobis pulled the cart the entire way (45 stadia; 8 km). Cydippe was impressed with their devotion to her and her goddess and asked Hera to give her children the best gift a god could give a person. Hera ordained that the brothers would die in their sleep.
Cydippe married Ochimus' brother, Cercaphus, who inherited the island.
According to an alternate version, Ochimus engaged Cydippe to Ocridion but Cercaphus loved her and kidnapped her. He didn't return until Ochimus was old.