This paper analyses mutual causalities between crude oil price and euro / US dollar exchange rate. Instead of focusing on long-run macroeconomic linkages like the bulk of the relevant literature takes a financial markets perspective using daily data. The fast-running simultaneousimpacts are identified through heteroscedasticity by specifying multivariate EGARCH processes for the structural variances. While for the decade after 1986 no significance is found, thereafter oil price changes cause inverse reactions of the dollar price and affect itsvolatility. Reversely, dollar appreciation asymmetrically increases the oil price.