He was born in to the family of Alexander Aleksandrovich Saveliev, a nobleman and leader of the zemstvo in Nizhny Novgorod who was a deputy of the Imperial State Duma for the Cadet Party.
Being very secretive with his revolutionary activities he worked under the pseudonyms Vetrov, Nikita, Valerian and Petrov which resulted in many party members assuming he was more than one person.
From 1921 to 1922 he was a member of the presidium and head of the editorial and publishing department of the Supreme Soviet of the National Economy and editor of its magazine.
In one of the leading articles, Saveliev argued that the Pope and the Bishop of Canterbury, defending the enemies-priests, were calling on the peoples of the world to a "crusade against the USSR."
[5] The main subjects to which his works were devoted are the theory of Marxism–Leninism, the history of the Party and the October Revolution, and the economy of the Soviet Union.
Saveliev's most famous works are "Ленин и Октябрьское вооруженное восстание" (Lenin and the October Armed Uprising) (1927) and "Возникновение большевизма" (The Emergence of Bolshevism) (1933).