After Second World War, demand for oil increased and in 1970s reached to its maximum growth. And naturally, providing this level of demand depended on much more import from OPEC, especially from Middle Eastern members. Contemporaneous, in the early 1970s, some OPEC governments stopped granting new concessions and starting to claim equity participation in the existing concessions, with a few of them opting for full nationalization. These two processes led to the introduction of new powerful actor to global oil market.
But, as the further events showed, OPEC's dominance had a short life and because of some reasons, chiefly as a result of OPEC's behavior after second oil shock (1979), this period shortly finished. In the mid 1980s, it's pronounced that the OPEC's formal prices catch to trouble.