They are returning to a virtually empty city where the 1st Marine Division's rumbling tanks and patrolling riflemen are out in force making sure the guerrillas don't come back.

American officers say only about a tenth of the 250,000 residents have returned since fleeing the weeklong battle in November that drove out insurgents who had controlled the predominantly Sunni Muslim city.

Signs scrawled on some houses proclaim ''Family leaves here'' or ''Family in the home,'' their inexpert English alerting the Marines that families have moved back in. White banners daubed with similar messages dangle from other homes.

Most buildings also have been marked by the Marines with map grid numbers and symbols denoting whether they have been searched.

With the electric grid still out, generators roar on every corner. Few shops are open. Some vendors sell fruit and vegetables from street stands, and kiosks offer gum.

Marines handed out military rations for weeks after the battle to help the few families in the city get by, but that stopped after the Jan. 30 national election. ''They have to get back on their own feet,'' said 1st Lt. Sven Jensen, leading a patrol from the 3rd Battalion, 5th Marines.

Checkpoints across Fallujah and around its edges control the flow of the city's people. Many come back for just a day, to check that their property is still in good order or to inspect any damage.

Marines are using some damaged buildings abandoned by families. The young Americans lift weights in one. In another, they have laid out a huge map of the city, using bricks to represent each house and building.

There is little activity on the streets. People sit outside their homes talking and watching. Bored Iraqis run outside to watch when tanks grumble past. Children cover their ears against the noise.

Marines patrol the streets constantly to reassure residents and to discourage insurgents. The Marines pay particular attention to young men who seem not to want to be noticed, pulling them aside to make quick mugshots in case of future troubles.

Jensen said the U.S. presence is paying off. After the battle, patrols often discovered big caches of weapons, he said. The haul last week: one automatic weapon found in the trunk of a vehicle.

''Safest city in Iraq,'' said one of his Marines, Cpl. Daniel Ferrari.