Final answer:
In the play 'Antigone', Eteocles and Polyneices are brothers who fight each other for the throne of Thebes, both meeting their demise, which greatly affects their sister, Antigone.
Step-by-step explanation:
The relationship between Eteocles and Polyneices in the play Antigone is that of brothers. These two characters are engaged in a bitter conflict over the throne of Thebes after their father, King Oedipus, falls from power. In the fierce battle for succession, both brothers end up killing each other, leaving a profound impact on their sister Antigone, the titular character of Sophocles' tragedy. Despite their fight, their familial bond remains a crucial element of the narrative.