This paper investigates the relationship between the volatility of the stock market and that of the nominal exchange rate in India. Using the E-Garch specification proposed by Nelson (1991) it addresses the question whether changes in the volatility of the stock market affects volatility in the foreign exchange market and vice versa. The model specification incorporates asymmetric effects of positive and negative returns surprises on volatility both in the same market as well as spillovers across the two markets. Empirical analysis with one of the major stock market indices supports the hypothesis of such volatility linkages while for the other index there appears to be a spillover from the foreign exchange market to the stock market but not the other way round.