In this research , statistical work in stochastic modelling of hydrologic time seriesrnis discussed. The theme is the comparison of stationarity and non-stationarity approachesrnfor stochastic simulation of monthly streamflow sequences. The paper first introducesrnvarious concepts related to stochastic modelling; the history of stochastic simulation andrnapplications of stochastic modelling in hydrology; and the step-by-step modellingrnprocedures. Then the paper describes how synthetic streamflow sequences can be generatedrnusing these procedures. As a particular case, synthetic streamflow sequences were generatedrnfor two streams in Ethiopia using both stationarity and non-stationarity approaches. At last,rnbased on these synthetic flows , an attempt was made to compare the performance of therntwo approaches with some comments and recommendations