The aim of this paper is to study the degree of interdependence between oil price and stock market index into two groups of countries: oil-importers and oil-exporters. To this end, we propose a new empirical methodology allowing a time-varying dynamic correlation measure between the stock market index and the oil price series. We use the frequency approach proposed by Priestley and Tong (1973), that is the evolutionary co-spectral analysis. This method allows us to distinguish between short-run and medium-run dependence. In order to complete our study by analysing long-run dependence, we use the cointegration procedure developed by Engle and Granger (1987). We find that interdependence between the oil price and the stock market is stronger in exporters׳ markets than in the importers׳ ones.