Jaya and Vijaya were not the Asur, so technically their story should not be included here among the Asur's stories, but their story is a prelude to several other Asur stories that is why it is included here. Jaya and Vijaya were the guards of Vishnu Bhagavaan.

Once Sanakaadi Muni came to Vaikunth to see Vishnu and wanted to enter Vishnu's palace, that His these guards stopped them to enter and asked them - "Who are you and what do you want?" Sanakaadi Muni do not look like Muni, they look like 5-year old children, that is why Jaya and Vijaya did not recognize them. Sanakaadi Muni got angry at this and said - "If you do not know us, you are not worthy to be the guards of Vishnu. Go and fall on Prithvi and be Raakshas." Hearing this both fell on Muni's feet.

Vishnu also heard some voices in high pitch, so He also came out of His palace and found Sanakaadi Muni standing at the gate. He welcomed them and asked them "What happened". Sanakaadi Muni told Him the whole incident. Vishnu asked their forgiveness and took them inside. Jaya and Vijaya also asked for their forgiveness. Seeing Vishnu's politeness, Sanakaadi Muni said to Him - "You yourself may decide their punishment." and they went away.

Vishnu asked Jaya and Vijaya - "You cannot escape from being Raakshas, but you have two options - one, you be Raakshas for seven lives and be my Bhakt; two, you be Raakshas for three lives and be my greatest enemy." Jaya and Vijaya thought for a moment and said - "Bhagavan, We do not like to part from your feet, so we would like to be on Earth only for three lives and your greatest enemy. But there is one request that when we take birth there we should be killed by you only and we should not forget our Gyaan." Vishnu said - "So be it."

Thus these Jaya and Vijaya in their first life were born as Hiranyakashyap and Hiranyaaksh in Sat Yug for whom Vishnu incarnated as Nrasinh Bhagavaan and Varaah and killed them. In their second life, they were born as Raavan and Kumbhkarn in Tretaa Yug. They both were killed by Raam. In their third and last life they were born as Shishupaal and Dantvakra in Dwaapar Yug and they both were killed by Krishn. In this life they got Mukti from their Shaap and returned to Vishnu's Lok.