In this paper we focus on how an international carbon treaty will influence the exploration of oil in Non-OPEC countries. We present a numerical intertemporal global equilibrium model for the fossil fuel markets. The international oil market is modelled with a cartel (OPEC) and a competitive fringe on the supply side, following a Nash-Cournot approach. An initial resource base for oil is given in the Non-OPEC region, however, the resource base changes over time due to depletion, exploration and discovery. When studying the effects of different climate treaties on oil exploration, two contrasting incentives apply. If an international carbon tax is introduced, the producer price of oil will fall giving an incentive to reduce oil production and exploration. However, the oil price may increase less rapidly over time, which gives an incentive to accelerate production, and exploration. In fact, in the case of a rising carbon tax, we find that the last incentive proves to be the strongest which means that an international carbon treaty accelerates oil exploration in Non-OPEC countries.