In Hurrian mythology, Kušuḫ appears as one of the allies of the weather god Teššub in his struggle against Kumarbi, but known compositions do not provide much information about his individual characteristics.

It has also been proposed that the Ugaritic composition Marriage of Nikkal and Yarikh was based on a Hurrian myth about Kušuḫ, well attested as the husband of this goddess.

[9][17] It has also been noted that Kuzina is only known from a single attestation in the so-called Tale of Appu, whose Hurrian origin is disputed, and researchers such as Itamar Singer consider it to have Hittite roots instead, though this view is not universally accepted either.

[4] In addition to Kušuḫ, a secondary name of the moon god in Hurrian sources was Umbu,[2] also spelled Umpu, Umpa and Umpi.

[21] In early scholarship it was assumed that Umbu was an appellative referring to Nikkal, analogous to the second element in the full Ugaritic form of her name, Nikkal-wa-Ib, but according to Giorgieri this is not plausible in the light of more recent research.

[2] However, a well attested role of Kušuḫ which according to Gernot Wilhelm sets him apart from his Mesopotamian counterpart was that of a protector of oaths, otherwise commonly associated with underworld deities in Hurrian culture.

[11] A depiction of Kušuḫ is known from the reliefs showing a procession of deities in the Yazılıkaya sanctuary, with the figure representing him being assigned the number 35 in scholarly treatments of this site.

[27] A possible artistic portrayal of Kušuḫ has also been identified on the golden bowl of Hasanlu, sometimes assumed to be a late example of art inspired by motifs from Hurrian mythology, on which a moon god is shown traveling in a chariot drawn by mules.

[4] Piotr Taracha points out that it might be significant that she was already linked with another lunar god, Saggar, in the third millennium BCE in Ma-NEki, as attested in texts from Ebla.

[29] A passage labeling Teššub as a son of Kušuḫ is known,[30] but as it is entirely isolated and no further known documents refer to such a connection between these two gods, Daniel Schwmer remarks that it is difficult to evaluate its significance.

[5] It has been proposed by Meindert Dijkstra that the god Tapšuwari was regarded as the sukkal (attendant deity) of Kušuḫ,[31] though he has also been interpreted as one of the members of the circle of Kumarbi.

[2] Kušuḫ was a high-ranking, commonly worshiped god,[35] and he is regarded by researchers as one of the "pan-Hurrian" deities, present in the pantheons of all areas where the Hurrian language was in use, from Kizzuwatna in modern Turkey to the Zagros Mountains, similar to Teššub, Šauška, Kumarbi or Nabarbi.

[4] He is among the members of the Hurrian pantheon depicted in the Yazılıkaya sanctuary, where he is placed between Šauška's handmaidens Ninatta and Kulitta and the sun god Šimige in the procession of deities following Teššub.

"[46] The name Umbu is attested in Hurro-Hittite context too: examples include oath formulas, where he paired with Šarruma, and texts pertaining the išuwa festival.

[54] Kušuḫ is also mentioned briefly in another myth dealing with the same conflict, the Song of Ullikummi, where Kumarbi states that he has to hide the eponymous stone monster somewhere where the allies of, including the moon god, will not be able to find him while he continues to grow.

[56] It is sometimes assumed that the Ugaritic myth about the marriage of the local moon god Yarikh and Nikkal (KTU 1.24) had Hurrian origin,[57][58] and according to Nicolas Wyatt it is possible that in a hitherto unknown earlier version the protagonist was Kušuḫ instead.