[2][3] In 1957 he graduated from the graduate Institute of State and Law of the Academy of Sciences of the USSR and defended the dissertation on competition of a scientific degree of candidate of legal Sciences on the topic "Legal issues of the strike movement in the United States.

In 1967 he defended his thesis for the degree of doctor of law on the topic "Social activities of the imperialist state: (Political and legal aspects)".

From 1967 to 1977 he worked as head of the Department of the Institute of international labor movement of the USSR Academy of Sciences.

[6] On 13 February 1995, Baglai was nominated for the post of President of the Constitutional Court for the first time, but lost the election to Vladimir Tumanov.

On 21 February 2003, Baglai's term expired and Valery Zorkin was elected the new President of the Constitutional Court.