Hypothesis of Market Efficiency is an important concept for the investors across the globe holding diversified portfolios. With the world economy getting more integrated day by day, more people are investing in global emerging markets. This means that it is pertinent to understand the efficiency of these markets. This paper tests for market efficiency by studying the impact of global financial crisis of 2008 and the recent Chinese crisis of 2015 on stock market efficiency in emerging stock markets of China and India. The data for last 20 years was collected from both Bombay Stock Exchange (BSE200) and the Shanghai Stock Exchange Composite Index and divided into four sub-periods, i.e. before financial crisis period (period-I), during recession (period-II), after recession and before Chinese Crisis (periodIII) and from the start of Chinese crisis till date (period- IV). Daily returns for the SSE and BSE were examined and tested for randomness using a combination of auto correlation tests, runs tests and unit root tests (Augmented Dickey-Fuller) for the entire sample period and the four sub-periods. The evidence from all these tests supports that both the Indian and Chinese stock markets do not exhibit weak form of market efficiency. They do not follow random walk overall and in the first three periods (1996 till the 2015) implying that recession did not impact the markets to a great extent, although the efficiency in percentage terms seems to be increasing after the global financial crisis of 2008.