They are twin brothers; Methone is the male and has a blue hair; Ymir is the female and has a red hair.
Like various animes where the brothers love each other, Ymir loves Methone and Methone loves Ymir; for each, his brother/sister the most powerful and beautiful person. Each one hates when his brother/sister is injured.
Ymir and Methone were sent to Jamir to kill Yuna. They use Laki as hostage and stops her time flow. Kouga arrives and convinces Yuna to fight again against the enemy; Yuna wears her cloth and Souma arrives, and Yuna and Souma defeat the pair, and Ymir helps Methone that is most injured, and gets away.
In Pallas Belda, Europa gives to Methone an artifact that can absorb anything to the user and fuses their powers; Methone uses the artifact to absorb Ymir, so, she dies; Methone become a fused being with two hair colors, and become most powerful. Methone blames Souma and Yuna (that goes fight against him and Ymir) to the death of his loved sister. Souma and Yuna with their powers, defeats Methone and Ymir's souls kills him.