During the past decades, the efficient market hypothesis (EMH) has been at the heart of the debate in the financial literature. Ultimately, the consequence of the efficiency of a market is that prices always fully reflect all available information. The objective of this study is to test whether the Stock exchange of Mauritius (SEM) and Development and Enterprise market (DEM) are weak form efficient. The autocorrelation test, variance ratio test, run test and calendar effects testing, made under OLS regression and GARCH-M were used to examine weak-form EMH. Two indices namely the DEMEX and SEMDEX are tested by using both daily and monthly return data for the period from 1st January 2007 to 31st October 2012. Results obtained are mixed. For instance, from the autocorrelation test shows evidence to reject the null hypothesis of random walk for both daily and monthly returns. On the other hand, the run test indicates that the null hypothesis of random walk is rejected only for daily returns of SEMDEX and DEMEX while not rejected for the monthly series. The Lo and MacKinley’s variance ratio test fails to support weak-form-efficiency. Under both a daily perspective as well as on a monthly one, the returns of DEMEX has consistently proven to follow a random walk by using OLS and GARCH. While SEMDEX proved otherwise.