A membrane bioreactor system for treating raw water or wastewater or activated sludge having a filtration tank in which at least one submerged filtration membrane module is situated in the filtration tank, wherein the raw water or wastewater or the activated sludge in the filtration tank contains non-porous, biologically resistant particles, a feed device for gas is provided for the bottom end of the filtration membrane module, the gas streaming moves the particles upward between the membranes, and the gas is compressed air.