Seven Asian stock markets (Japan, South Korea, Singapore, China, Indonesia, Malaysia and Philippines) were tested by using two methodologies. First, cointegration method tested the long run relationship among stock prices, dividends and earnings. Second, duration dependence method tested the hazard rate. The conclusion of this research is that rational speculative bubbles existed in the Chinese, Indonesian and Malaysian stock markets, but not in Japan, Singapore, Korea and Philippines over the sample period from 1991 to 2009; and the presence of rational speculative bubbles is more prevalent in emerging than developed stock markets. Further sub-period analysis shows that the rational speculative bubbles existed mainly during the pre-financial crisis sub-period, but not in post-financial crisis sub-period. In the case of the duration dependence test, weekly data was more sensitive than monthly data in detecting speculative bubbles.