The Russians stay inside their heavily defended positions in order to avoid clashes with the locals fighters who are intimately familiar with the terrain.
But there is also a balance of fear between the two sides who make efforts to avoid each other. On a recent evening we walked unnoticed for several hours parallel to the federal troops' positions.
The Russians surround their posts with armoured cars and keep the headlights switched on to light up the area around them. Of course, they do it out of fear of being attacked at night. But the brightly lit, bustling scene is like Kutuzovsky Prospekt (Moscow's main thoroughfare) in the week before Christmas.
With the engines grumbling, the soldiers did not hear as the Chechen fighters walked right past their positions. The road is barely visible and churned up by the caterpillar tracks of the armoured cars.
We stumbled and fell noisily, but we passed all the Russian posts and the guerrillas greeted a group of armed Chechens coming in the other direction.
The village of Kater-Yurt, 20 miles (30 kilometres) south- east of Grozny, has become a kind of safe zone which has attracted refugees from all over Chechnya. So far, about 10,000 have made their way here.
Under pressure from the Russians, the local elders managed to persuade the Chechen fighters to leave, allowing Russian interior ministry troops to comb the village to make sure they had gone.
Five women arrived in the village yesterday after crawling along a dry riverbed by night, from the village of Alkhan-Yurt, which is 10 miles (15 kilometres) away. They said that in Alkhan-Yurt, there were many dead because federal soldiers had been throwing grenades into basements; corpses lay in the cellars and out on the streets because there was nobody to bury them.
Andrei Babitsky is a journalist with Radio Liberty.Reuse content