The relationship between the temporal evolution of the commodity market and the stock market has long term implications for policy makers, and particularly in the case of emerging markets, the economy as a whole. We analyze the complex dynamics of the daily variation of two indices of stock and commodity exchange respectively of India. To understand whether there is any difference between emerging markets and developed markets in terms of a dynamic correlation between the two market indices, we also examine the complex dynamics of stock and commodity indices of the US market. We compare the daily variation of the commodity and stock prices in the two countries separately. For this purpose we have considered commodity India along with Dow Jones Industrial Average (DJIA) and Dow Jones-AIG Commodity (DJ-AIGCI) indices for stock and commodities, USA, from June 2005 to August 2008. To analyse the dynamics of the time variation of the indices we use a set of analytical methods based on recurrence plots. Our studies show that the dynamics of the Indian stock and commodity exchanges have a lagged correlation while those of US market have a lead correlation and a weaker correlation.