Eutychius does not seem to know that much about the next two Ummayad caliphs, so I include both of their short entries here.
CALIPHATE OF YAZID IBN MU`AWIYA (60-64/680-683)
1. The bay’ah was given to Yazid ibn Mu’awiya b. Abi Sufyan – his mother was Maysūr, daughter of Yahdak al-Kalbi -, in the month of Ragab in the sixtieth year of the Hegira. At Karbalah, in Iraq, on the tenth of the month of al-Muharram of the sixty-first year of the Hegira, at the age of sixty-three years old, al-Husayn, son of Ali ibn Abi Talib was killed. His head was taken to Damascus and carried around the city. After the killing of al-Husayn, son of Ali ibn Abi Talib, there rose up at Mecca Abdullah ibn az-Zubayr b. al-Gharrām, who proclaimed himself caliph, – his mother was Asma, the daughter of Abu Bakr, the just – This was the beginning of his rebellion.
2. Yazid ibn Mu’awiya died after three years and eight months of his caliphate. After him there ruled, for only forty days, his son Yazid ibn Mu’awiya b. Mu’awiya . The leaders of his bodyguard were first Hamid ibn Kharba b. Yahdak al-Kalbi and then Amir ibn Abd Allah al-Hamdani. His ‘hagib‘ was the freedman Safwan.
CALIPHATE OF MARWĀN IBN AL-HAKAM (64-65/684-685)
1. The bay’ah was given to Marwan ibn al-Hakam b. Abi’l-`Ās b. Umayya b. Abd Shams – his mother was Amina, daughter of Alqama Safwan ibn al-Kināni -. in the month of Ragab in the sixty-fourth year of the Hegira, while Abdullah ibn az-Zubayr continued his well-fortified opposition at Mecca. Neither the inhabitants of Damascus nor those of Palestine could make a pilgrimage to Mecca because Marwan ibn al-Hakam had forbidden them to, because of Abdullah ibn az-Zubayr. Then there was the battle of Marg-Rahit with ad-Dahhak ibn Qays al-Fahri.
2. Marwan ibn al-Hakam died in the month of Rabi al-awwal in the sixty-fifth year [of the Hegira]. He was caliph for nine months and died at the age of sixty-one. He was tall, tanned and had blue eyes. He was buried in Damascus. The leader of his bodyguard was Yahya ibn Qays al-Assāni and his hagib was Abu Sahl al-Aswad, the freedman of his mother.