While enrolled at university in Zagreb in 1933, he joined the then-underground Communist Party of Yugoslavia and was subsequently arrested and served six months in prison for his pro-communist writings in the city of Ptuj.

Upon his release, he briefly went to Ljubljana to study law but returned to Ptuj due to an illness and began working full time as an organizer for the communist party.

[2] Following the war, he continued his career in the Yugoslav People's Army and from 1946 to 1948 attended the K. Е. Voroshilov Higher Military Academy in the Soviet Union.

Upon his return, Kveder was appointed deputy commander of the Belgrade Military Academy and also served as editor in chief of the newspaper Vojno delo.

Kveder began his political career in 1945 when he became Governor of Zone B of the Free Territory of Trieste, then jointly occupied by the Allies and Yugoslavia.