This study tests for martingale difference hypothesis (MDH) in nine selected Foreign Exchange (FX) markets from Asia–Pacific countries. Its main contributions to the literature include: (i) it adopts recent techniques in both the Autocorrelation based and Spectrum based tests for MDH, namely; the Wild Bootstrap Automatic Variance Ratio test by Kim (2009) and the Wild Bootstrap Generalized Spectral test by Escanciano and Velasco (2006); (ii) it determines structural breaks endogenously for all the returns series using Perron (2006) unit root test with structural break, and (iii) based on the Perron results, it obtains two sub-samples and thereafter tests for MDH. Empirical result from this study shows that FX market efficiency could be inconsistent over time due to changes in policies and events. Thus, a preliminary test for the presence significant structural break may be necessary when testing for MDH.