[1] A soldier at the Serbian court, he helped overthrow the Obrenović dynasty with the assassination of King Alexander I of Serbia (11 June), which was orchestrated by Colonel Dragutin Dimitrijević, the founder and leading member of the secret nationalist organization Black Hand.

[2] In 1921, King Alexander I of Yugoslavia appointed Živković commander of the Royal Guard, but he was briefly demoted due to accusations by a young guardsman that he tried to seduce him.

Živković held the office as a member of the Yugoslav Radical Peasants' Democracy (JRSD), which became the only legal party in Yugoslavia, following electoral reforms.

As a prime minister he did not enjoy high regard by either the military or among other politicians not only due to his widely rumoured homosexuality.

In 1946 he was tried in absentia in the Federal People's Republic of Yugoslavia at the Trial of Mihailović et al. and sentenced to death by the communist authorities.