[1][2] Galazov was born in Pravoberezhny District, at the time part of the Soviet Union.

[1][2] In 1938 his father Hadzhimurza Ilyasovich was illegally detained by the Soviet government and several years later died in prison.

From 1952-1958 he worked as a teacher of Russian language and literature and was director of studies at Humalagskoy Secondary School.

From 1958 to 1959 he was superintendent of schools of the Ministry of Education of the Soviet Socialist Republic of North Ossetia.

In January 1994, he was elected the first president of the Republic of North Ossetia and held the position until 1998.