Efficiency is not an easy thing. From that point, this topic is attracting lots of competitors, investors researchers, and students in both mathematics and economics departments. Like everything in this life, there is gain and loss so efficiency has different effects on investors and financial companies Our objective in this thesis is to investigate Fama's Efficiency hypothesis for some stocks in Beirut Stocks Exchange. We will use both Runs test which tests the randomness of the series and the other test is the ADF test that including other tests such as ( KPSS and PP test ) and it gives us a clue about the stationarity of the series.