Bleyan graduated from Yerevan State University as a physicist.
After serving as vice president in the Yerevan Municipality's Executive Committee, he was elected to the Armenian Parliament in 1990.
Between 1994 and 2002, he served as president of the New Path (in Armenian «Նոր ուղի») political party.
He was imprisoned in 1999 (the charges were: civil and criminal offences, including embezzlement).
His lawyer complained to the European Parliament that he has been beaten and placed in solitary confinement.