This paper examines the random walk (RW) and the martingale difference sequence (MDS) processes for the Australian dollar and seven Asian currencies relative to three benchmark currencies between 1993 and 2008. We use Wright’s (2000) non-parametric variance ratio test for the RW and Kuan and Lee’s (2004) test for the MDS. The results show that (i) the hypotheses of RW and MDS are rejected for all eight currencies for the entire study period as well as for the sub-period leading up to the Asian financial crisis in 1997; (ii) for the sub-period following the Asian crisis, only the Australian dollar and Korean won behave as weak-form efficient while the six other Asian emerging currencies show no discernible improvement toward market efficiency; (iii) on balance, the rejection of random walk is more robust by Kuan and Lee’s martingale test as compared to that by Wright’s sign and rank variance ratio test.