This paper aims at reassessing the empirical relationship between the real price of oil and the U.S. dollar real effective exchange rate over the 1974-2015 period. We find that changes in both variables are now linked by a negative relationship, going from the dollar exchange rate to the real oil price. However, the same relationship is found positive when ending the sample in the mid-2000s, in line with the previous literature. To understand and investigate this evolution, we rely on a nonlinear, smooth transition regression model in which the oil price-dollar nexus depends on the dynamics followed by the U.S. currency. Our results show that the relationship is negative most of the times but turns positive when the dollar hits very high values, as in the early eighties