Indian stock market has attracted foreign investors as a developing market with potential return expectations and in particular, the Indian IT sector has notched a top place in the world. This paper examines the boom in the market to identify the presence of rational speculative bubbles in the S&P CNX NIFTY and CNX IT INDEX during the period 1999 to 2006. There has been a mark up on asset prices generated by self-sustaining expectations without any fundamental justification. However markets seem to have made corrections to match the fundamental expectations. We apply both indirect and direct specification tests to detect bubbles and the empirical results reject the null hypothesis of no bubbles and the models confirm the presence of rational speculative bubbles.