The Kridakhanda of the Ganesha Purana narrates the stories of four incarnations (Avatars, Sanskrit:अवतार; avatāra) of Ganesha, each of which appeared in the four different yugas.[10][11] The explanation of the incarnations of Ganesha is shown in the verses in the 132nd chapter of Kridakhanda of Ganesha Purana. It says,These four are not the same as the eight incarnations of Ganesha that are described in the Mudgala Purana.
Mahotkata Vinayaka (Mahotkaţa Vināyaka), who has ten arms and a red complexion. Different sources list his mount (vāhana) as either an elephant or lion. He was born to Kashyapa (Kaśyapa) and Aditi in the Krita yuga. The name Kāśyapaḥ (descendant of Kaśyapa) for Ganesha refers to this incarnation.[12] This incarnation killed the demon brothers Narantaka (Narāntaka) and Devantaka (Devāntaka), as well as the demon Dhumraksha (Dhūṃrākşa).
Mayuresvara (Mayūreśvara), who has six arms and a white complexion. His mount is a peacock. He was born to Shiva and Parvati in the Treta yuga. He incarnates for the purpose of killing the demon Sindhu. At the end of this incarnation he gives his peacock mount to his younger brother Skanda, with whom the peacock mount is generally associated.
Gajanana (Gajānana), who has four arms and was born with a red complexion. He has a mouse as his mount. He is born to Shiva and Parvati in the Dvapara yuga. He incarnates for the purpose of killing the demon Sindura (Sindūra), who was so-named due to his reddish-pink complexion (see: Sindoor). It is during this incarnation that Ganesha gives the discourse known as the Ganesha Gita to King Varenya.
Dhumraketu (Dhūmraketu) is grey in colour, like ash or smoke (dhūmra). He has either two or four arms.[13] He has a blue horse as his mount. He will come to end the decline of the Kali yuga. During this incarnation he kills numerous demons. Grimes notes that there is a parallel between this incarnation of Ganesha and the tenth and final incarnation of Vishnu, where he will ride upon the white horse Kalki. The other difference is, Lord Vigneshwara tells Varenya that the whole universe and all the deva are created by him and ultimately everything will come back to him.