The paper will summarize the historical record of hydrocarbon discovery in the United States and emphasize that for conventional oil both discovery and production rates have peaked.  Comments will be made on the situation relating to gas discovery and production.  The significance of the discovery of the major Alaskan fields at Prudhoe Bay and Kuparuk will be discussed and the history of Prudhoe Bay in particular will be used to assess the potential for new technology to bring about ‘reserves growth’ in existing fields.  The potential of the essentially unexplored Alaskan National Wildlife Reserve (ANWR) to counteract in the declines in production from the ‘Lower’48 states will be assessed.  It will be concluded that the US has no possibility of being self-sufficient in oil supply without radical cuts being made in oil demand.