The present paper examines the characteristics of return volatilities in the equity market and the index futures market in India. Volatility in the NSE Nifty index and that in its futures market are both seen to exhibit features of mean reversion, volatility clustering and a fair degree of volatility persistence, estimates of which give an idea of the impact and duration of a particular information shock to the market. The returns volatility is found to exhibit significant asymmetric response in times of market retreats and advances, with volatility arising in times of market decline being much sharper and more persistent. The study also provides evidence of volatility linkages between the spot and futures markets. Contemporaneous transmission effects across volatilities of the Indian (NSE) Stock and Index futures markets are tested on daily data, using an asymmetric (threshold) GARCH framework. These results have implications for understanding the pattern of information flows between the two markets. The results indicate that the futures market plays a leading role in assimilating information and thus moderating, though to a small extent, the spot market volatility.