In this paper, we explore linear and nonlinear Granger causalities between oil price and the real effective exchange rate of the Indian currency, known as ‘rupee’. First, we apply the standard time domain approach, but fail to find any causal relationship. So, we decompose the two series at various scales of resolution using the wavelet methodology in an effort to revisit the relationships among the decompose series on a scale by scale basis. We also use a battery of non-linear causality tests in the time and the frequency domain. We uncover linear and nonlinear causal relationships between the oil price and the real effective exchange rate of Indian rupee at higher time scales (lower frequency). Although we do not find causal relationship at the lower time scales, there is evidence of causality at higher time scales only.