There is now a voluminous literature investigating the issue of market efficiency, particularly in relation to the weak-form type of efficiency, which are based on autocorrelation tests. However, the results from this literature are mixed. There is a concern, however, that the autocorrelation tests used in these studies could have suffered from problems and biases arising from heteroskedasticity in the data. Over the last 15 years, financial markets have suffered from a number of crises which may have intensified the presence of heteroskedasticity in financial data. In this paper, we examine the efficiency of Asian markets based on two newly-developed tests - the Escanciano and Lobato (2009)'s automatic Box-Pierce Qk test and Nankervis and Savin (2010)'s generalised Andrews-Ploberger test, which are robust to heteroskedasticity. Asia provides an interesting context as it has been the economic growth region over the last three decades but yet its financial markets are deemed to lag behind in terms of development. However, since the late 80s, it has implemented liberalisation and deregulation programs which were aimed at improving the functioning of its financial markets. Thus, it is debated as to whether or not Asian financial markets are or have become efficient. We examine 16 markets consisting of 5 developed, 9 emerging and 2 frontier ones. We confirm that all the developed markets are efficient while the frontier ones are all inefficient and mixed for the less developed ones. We also find that the level of efficiency of these markets varies over time - decreasing during the GFC and then increasing afterwards.