In this paper we first study the statistical characteristics of the major Egyptian stock market indices, i.e. EGX 100, EGX 70 and EGX 30, using descriptive statistics, stationarity tests and power spectrum analysis. After that, we use Brock-Dechert-Scheinkman (BDS) test to detect the nonlinearity in these indices after removing their linear dependence using traditional ARIMA models (or just taking a first difference of natural logarithms).