Essentially, there was no parallel system of semi-cooperative, semi-competitive "secular" and "ecclesiastical" authorities like in the Catholic world. Orthodox states such as Byzantium and Muscovy did attempt to suppress heresy, but there was no independent authority like the papacy to say stuff like "you're being too lenient -- take sterner measures or be excommunciated," or "you're being to drastic -- you need to give people more of a chance to prove innocence and/or repent."

Orthodox suppression of heresies like the Bogomils or the Sect of Skhariya the Jew involved collaboration between local Orthodox bishops and secular princes, but there was no sort of super-authority that stretched from Novgorod to Constantinople and stood outside of the normal worldly power structure.