A process for operating filtering membranes submerged in a tank involves, in one aspect, periodically deconcentrating the tank by at least partially emptying and refilling the tank with fresh water while permeation continues. In another aspect, long trains of membrane modules are placed in series along a flow path in the tank. In one embodiment, constant aeration is provided to prevent tank water from by-passing the membrane modules while proving controlled mixing such that the average concentration of solids in the tank is lower than the concentration of solids in the tank near an outlet for removing retentate from the tank. In another embodiment, the membrane modules are arranged in a series of filtration zones between a feed water inlet and a retentate outlet of a tank. Permeate is withdrawn from the filtration zones by separate means associated with each filtration zone. Tank water containing rejected solids flows in a tank flow through the filtration zones, increasing in concentration from one zone to the next. A preferred membrane module has membranes transverse to the tank flow and fills a substantial portion of each filtration zone. With either embodiment, aeration, backwashing or packing density of membranes varies between filtration zones and the flow pattern in the tank may be periodically reversed.