Eurysthĕnes in Harpers Dictionary of Classical Antiquities
（Εὐρυσθένης). A son of Aristodemus, who reigned conjointly with his twin-brother Procles at Sparta. It was not known which of the two was born first; the mother, who wished to see both her sons raised on the throne, refused to declare it; and they were both appointed kings of Sparta by order of the oracle of Delphi, B.C. 1102. After the death of the two brothers, the Lacedaemonians, who knew not to what family the right of seniority and succession belonged, permitted two kings to sit on the throne, one of each family. The descendants of Eurysthenes were called Eurysthenidae, and those of Procles, Proclidae. It was inconsistent with the laws of Sparta for two kings of the same family to ascend the throne together, yet that law was sometimes violated by oppression and tyranny. Eurysthenes had a son called Agis , who succeeded him. His descendants were called Agidae. There sat on the throne of Sparta thirty-one kings of the family of Eurysthenes, and only twenty-four of the Proclidae. The former were the more illustrious (Herod.iv. 147Herod., vi. 52; Pausan. iii. 1).
Eurysthenes in Wikipedia
In Greek mythology, Eurysthenes (Greek: Εὐρυσθένης) was one of the Heracleidae, a great-great-great-grandson of Heracles, and a son of Aristodemus. His twin was Procles, and together they received the land of Lacedaemon after Cresphontes, Temenus and Oxylus captured the Peloponnesus. He was the mythic founder of the Agiad dynasty of the Kings of Sparta, and father of his successor, Agis I.
Eurysthenes is also the name of one of the sons of Aegyptus. He was killed by his wife, *Monuste (name uncertain), one of the Danaids.