In Greek mythology, Eurystheus (pronounced //, Εὐρυσθεύς meaning "broad strength" in folk etymology and pronounced [eu̯rystʰěu̯s]) was king of Tiryns, one of three Mycenaean strongholds in the Argolid, although other authors including Homer and Euripides cast him as ruler of Argos: Sthenelus was his father and the "victorious horsewoman" Nicippe his mother, and he was a grandson of the hero Perseus, as was his opponent Heracles. He was married to Antimache, daughter of Amphidamas. In the contest of wills between Hera and Zeus over whose candidate would be hero, fated to defeat the remaining creatures representing an old order and bring about the reign of the Twelve Olympians, Eurystheus was Hera's candidate and Heracles — though his name implies that at one archaic stage of myth-making he had carried "Hera's fame" — was the candidate of Zeus. The arena for the actions that would bring about this deep change are the Twelve Labors imposed on Heracles by Eurystheus. The immediate necessity for the Labours of Heracles is as penance for Heracles' murder of his own family, in a fit of madness, which had been sent by Hera; however, further human rather than mythic motivation is supplied by mythographers who note that their respective families had been rivals for the throne of Mycenae. Details of the individual episodes may be found in the article on the Labours of Heracles, but Hera was connected with all of the opponents Heracles had to overcome.
Heracles' human stepfather Amphitryon was also a grandson of Perseus, and since Amphitryon's father (Alcaeus) was older than Eurystheus' father (Sthenelus), he might have received the kingdom, but Sthenelus had banished Amphitryon for accidentally killing (a familiar mytheme) the eldest son in the family (Electryon). When, shortly before his son Heracles was born, Zeus proclaimed the next-born descendant of Perseus should get the kingdom, Hera thwarted his ambitions by delaying Alcmene's labour and having her candidate Eurystheus born prematurely.
Heracles' first task was to slay the Nemean Lion and bring back its skin, which Heracles decided to wear. Eurystheus was so scared by Heracles' fearsome guise that he hid in a subterranean bronze winejar, and from that moment forth all labors were communicated to Heracles through a herald, Copreus.
For his second labour, to slay the Lernaean Hydra, Heracles took with him his nephew, Iolaus, as a charioteer. When Eurystheus found out that Heracles' nephew had helped him he declared that the labour had not been completed alone and as a result did not count towards the ten labours set for him.
Eurystheus' third task did not involve killing a beast, but to capture the Cerynian Hind, a golden-horned stag sacred to Artemis. Heracles knew that he had to return the hind, as he had promised, to Artemis, so he agreed to hand it over on the condition that Eurystheus himself come out and take it from him. Eurystheus did come out, but the moment Heracles let the hind go, she sprinted back to her mistress, and Heracles departed, saying that Eurystheus had not been quick enough.
When Heracles returned with the Erymanthian Boar, Eurystheus was frightened and hid again in his jar and begged Heracles to get rid of the beast; Heracles obliged.
The fifth labour proposed by Eurystheus was to clear out the numerous stables of Augeias. Striking a deal with Augeias, Heracles proposed a payment of a tenth of Augeias' cattle if the labour was completed successfully. Not believing the task feasible, Augeias agreed, asking his son Phyleus to witness.
Heracles rerouted two nearby rivers (Alpheis and Peneios) through the stable, clearing out the dung rapidly. When Augeias learned of Heracles' bargain for the task, he refused payment. Heracles brought the case to court, and Phyleus testified against his father. Enraged, Augeias banished both Phyleus and Heracles from the land before the court had cast their vote. However, Eurystheus refused to credit the labour to Heracles, as he had performed it for payment.
For his seventh labour Heracles captured the Cretan Bull. Heracles used a lasso and rode it back to his cousin. Eurystheus wanted to sacrifice the bull to Hera his patron, who hated Heracles. She refused the sacrifice because it reflected glory on Heracles. The bull was released and wandered to Marathon, becoming known as the Marathonian Bull.
When Heracles brought back the man-eating Mares of Diomedes successfully, Eurystheus dedicated the horses to Hera and allowed them to roam freely in the Argolid. Bucephalus, Alexander the Great's horse, was said to be descended from these mares.
To extend what may have once been ten Labours to the canonical dozen, it was said that Eurystheus didn't count the Hydra, as he was assisted, nor the Augean stables, as Heracles received payment for his work. For the eleventh labour Heracles had to steal the Apples of the Hesperides; his final labour was to capture Cerberus, the three-headed hound that guarded the entrance to Hades.
After Heracles died, Eurystheus attempted to destroy his many children (the Heracleidae, led by Hyllus), who fled to Athens. He attacked the city, but was soundly defeated, and he and his sons were killed. The stories about the killer of Eurystheus and the fate of his corpse vary, but the Athenians believed the burial site of Eurystheus remained on their soil and served to protect the country against the descendants of Heracles, who traditionally included the Spartans and Argives.
After Eurystheus' death, the brothers Atreus and Thyestes, whom he had left in charge during his absence, took over the city, the former exiling the latter and assuming the kingship, while Tiryns returned to the overlordship of Argos. It is also widely believed that after his death, Eurystheus's head shrivelled to resemble that of a duckling.
Eurystheus in Euripides 
Eurystheus was a character in Heracleidae, a play by Euripides. Macaria, one of the daughters of Heracles, and her brothers and sisters hid from Eurystheus in Athens, ruled by King Demophon. As Eurystheus prepared to attack, an oracle told Demophon that he would win if and only if a noble woman was sacrificed to Persephone. Macaria volunteered for the sacrifice and a spring was named the Macarian spring in her honor. Eurystheus speaks prophetically of his burial within Attica, claiming that he will be an anti-hero of sorts, though one who will eventually protect the Athenians.
- Antimache (Ἀντιμάχη), "strife of opposites" does not feature further in Greek myth, aside from a list of names of her sons and a genealogy for her, given in Pseudo-Apollodorus, Bibliotheke 2.5.9, 2.8.1, 3.9.2.
- See Carl A.P. Ruck and Danny Staples, The World of Classical Myth (1994) VII. "Herakles: Making the New Olympia", pp.163-202.
- Walter Burkert, Greek Religion (1985) p. 210: "Heracles seems to carry Hera's name in his own, as if Hera were his fame (kleos), yet all we ever hear is that from beginning to end,this jealous wife of Zeus persecutes her step-son with unrelenting hatred." For Hera's connection with each of Heracles' opponents, see under the individual Labours.
- Pseudo-Apollodorus, Bibliotheke 3.8.1 and Diodorus Siculus 4.57 give Hyllus as the slayer, Pausanias 1.44.10 and Strabo 7.6.19 give Iolaus.
- Heracleidae vv. 1026-1044.
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- Kerenyi, Karl. The Heroes of the Greeks. New York: Thames and Hudson, 1959.