According to the institution Békesi's material conditions were not provided for his learning, because his father died early.

He joined to the MSZMP in 1968 and he was appointed head of the financial department and later general deputy chairman of the Council of Pest County.

He became economical vice president of the Capital Council of Budapest in 1975 and member of the Committee of Planning Board.

His speciality is the councils' farming from the collegiate years, later this was supplemented by the public finance and the questions of the fiscal systems.

He was appointed titular university professor in 1981, during that time also served as economic-political secretary of the party's Committee of Budapest.