Major changes in the Norwegian exchange rate have often coincided with large fluctuations in the price of crude oil. Previous empirical studies have however suggested a weak and ambiguous relation between the oil price and the exchange rate. In contrast to these studies, this paper explores the possibility of a non-linear relation between the oil price and the exchange rate. An examination of daily observations reveals a negative relation between the oil price and the nominal value of the currency. The strength of this relation depends on whether the oil price is below, inside or above the range of 14-20 US dollars a barrel. Moreover, it depends on whether the oil price is displaying a falling or rising trend. The relation is relatively strong when oil prices are below 14 dollars and are falling. These non-linear effects are tested and quantified within equilibrium correcting models of the exchange rate, derived on monthly and quarterly data to control for the influence of other macroeconomic variables. The models with non-linear oil price effects outperform similar models with linear oil price effects. The latter models grossly underestimate the exchange rate response to oil price changes in a state of low oil prices. The paper undertakes an extensive evaluation of the derived models to demonstrate the robustness of the results.