Stock market indices are recognised as barometers of economic performance. While stock markets themselves can vary from one another, the corresponding indices can also differ on a variety of factors. In a globalised world it has become customary to address the issue of integration of markets around the world. In this paper the authors have tried to tackle this issue from the viewpoint of stock markets in India. The present work considered seven major international stock indices viz. – the Dow Jones Industrial Average and the NASDAQ Composite in the USA, the FTSE 100 in the UK, DAX in Germany, Nikkei 225 in Japan, Hang Seng in Hong Kong and the S&P/TSX Composite in Canada. On the domestic side the authors chose the Sensitive Index or Sensex. Using ten year data they attempted to determine whether a long-term relationship exists between the Indian markets and leading markets across the globe. For this purpose they utilised techniques like unit root testing, cointegration analysis and Granger causality analysis. The results indicated that the Sensex was influenced by all the leading international indices. However the converse did not necessarily hold true.