This research examines the weak-form efficiency in the Egyptian (ESE) and Saudi (SSE) Stock Markets. A set of parametric and non-parametric tests detect linear serial dependence in the two markets. We test the data for daily, weekly, and monthly data between January 1, 2000, and February 28, 2023, of two composite indices (EGX30 for ESE and TASI for SSE). Normality is tested using Skewness, Kurtosis, Jarque-Bera, Kolmogorov-Smirnov (K.S.) and Studentized Range tests, whereas random walk is tested using the non-parametric Runs test. Stationarity is tested using Augmented Dickey-Fuller (ADF), Phillips-Perron (P.P.) and KPSS tests. The empirical results indicate that the two stock market returns are abnormal. It doesn't behave randomly under the Runs test based on daily frequencies but randomly based on a monthly frequency. The two stock market returns are stationary.