The Heraclidae were the descendants of Heracles. They claimed the kingship of much of the Peloponessus as the inheritance of their ancestor. Their invasion is used to mythologically explain the invasion of the Dorians.
Exil from the Peloponessus
After the death of Heracles, his children escaped the clutches of the pursuing Eurystheus and eventually settled in Athens. Eurystheus attempted an invasion of Athens but was soundly defeated and slain. They escaped to Thessaly and were then adopted by the chief of the Dorian peoples; Aegimius. Heracles' son Hyllus was adopted by Aegimius, married his daughter and succeeded him as king of the Dorians. Hyllus received a prophecy that if he "waited for the third fruit' and entered by "the narrow passage by sea" he would be victorious. After three years Hyllus invaded the Peloponessus via the Isthmus of Corinth, to attack Atreus, Eurystheus' successor but was slain in single combat by King Echemus of Arcadia in single combat.
Second and Third Generations
The Heraclidae returned to Thessaly under the leadership of Cleodaeus, Hyllus' son. He also led an attack but was killed. He was succeeded by his son Aristomachus, who also failed.
Aristomachus' three sons, Temenus, Cresphontes and Aristodemus, approached the oracle and complained about the advice. They were told that the "third fruit" means the third generation after Hyllus,and the "narrow straits" were infact the Straits of Rhium. They were also advised to look for a three-eyed man. Temenus found a man named Oxylus, riding on a one-eyed horse. The fleet assembled at Naupactas but was delayed when Aristodemus was killed by a lightning bolt, for having killed a soothsayer. The invasion was carried out by Procles and Eurysthenes (Aristodemus' twin sons) in his place. The armies killed Tisamenus, son of Orestes, and divided the land between them; Sparta for Procles and Eurysthenes, Argos for Temenus, Pylos for Cresphontes and Pisa for Oxylus. Thus the Heraclidae ended up ruling the rightful inheritance of their great ancestor.
The descendants of Heracles and Omphale (queen of Lydia) reinstated their line as kings of Lydia in the fifth generation as well. They ruled in Lydia for 550 years with 22 kings, until the Gygid Dynasty took over.