Structural changes occurring in the crude oil market have stimulated the emergence of hypotheses suggesting that the relationship between prices of this raw material and the US dollar exchange rate can gradually become similar to that observed between oil prices and exchange rates of the currencies of the countries whose revenues from the export of this resource are a significant part of their current account balance. The purpose of this study was to determine and evaluate the time-varying dependence between oil prices and the exchange rate of the US dollar in the context of the same relationship for the Chinese, European, Japanese, Saudi, and Russian currencies. The results of our analyses implicate that a negative correlation between the variables in question grows stronger in time periods preceding global shocks and during thereof. The dominance of the USD in the crude oil market is reflected in similar characteristics of the correlations of the currencies of other countries, such as China, countries of the Euro area, or Japan. As for countries exporting crude oil, the situation varies. The results of our research suggest the lack of a stable relationships between prices of crude oil and currency exchange rates. It is also impossible to observe a long-term, unequivocal tendency of the currencies of oil exporting countries being positively correlated with oil prices. Russia was the closest to this situation. In Saudi Arabia, a positive correlation emerged during moments of crisis.