It has been investigated that dynamical evolutions of spatial optical solitons i n dissipative photorefractive systems based on two-wave mixing with a moving gra ting. Numerical results show that the stability of rigid photorefractive hologra phic solitons in such systems depends strongly on the system parameters. The sol iton for some sets of system parameters can propagate stably in the crystal over a distance that is long enough. The larger the ratio of the phase to intensity coupling coefficient of two-wave mixing, the better the stability of solitons. P otential application in optical switches, repeaters or splitters is discussed.