Russia declared victory in Chechnya, but the conflict isn't over. After this background report, two experts examine the conflict over the breakaway republic.

JIM LEHRER: Now, our Chechnya update begins with three reports on the Russian advance into Grozny over the past three weeks. The reporter is Julian Maynon of Independent Television News. (Gunfire)

JULIAN MANYON: Savage fighting is taking place in Grozny, with Russian troops renewing their drive toward the city's center from two directions. Battling in from the suburbs, the Russian target is a key bridge linking the two halves of the Chechen capital. And the aim seems to be to cut the rebel-held area in two. The Russians claim to be approaching the bridge and to have control of part of central Grozny. The latest pictures smuggled out of Grozny show the rebels in control of the central zone, but the Chechens acknowledge that there is now heavy fighting in the area.

In spite of massive Russian firepower, the rebels remain confident, and they appear to believe that their best strategy is to try to cause heavy Russian casualties with ambushes and sniper attacks. Russian television pictures show civilians emerging from the ruins, mainly the old and infirm. They have been unable to flee the fighting, and with no light, heating, or proper food supplies, their struggle for survival is not yet over. The Russian army has seized control of much of central Grozny, but their prize is a wasteland of rubble. What were once apartment blocks are now gutted shells.

The Russian advance followed an overnight withdrawal by Chechen rebels who attempted to break out of the city. In the southern part of Grozny, all that remains are the bunkers from which they mounted a fierce defense in more than a month of bitter fighting. Rebel spokesmen claim that all their troops have left the city in a planned, orderly operation. But the Russians deny that any major breakout has taken place, and say that several hundred rebels are still trapped in the northern section of the Chechen capital and will be destroyed if they do not surrender.

What is clear is that the rebels have suffered serious casualties in the last 24 hours. They themselves admit that the mayor of Grozny and two senior officers have been killed. And the Chechens have now confirmed that their most feared commander, Shamil Basuyev, was badly wounded in a land mine explosion as he attempted to lead his men out of Grozny. Russian troops are now raising their flag in some parts of the city and celebrating what they say will soon be complete control.

In order to save Grozny, the Russian army has destroyed it. Russian TV teams have been permitted to film in the smashed center of the city, now firmly under army control. Their pictures show almost unbelievable devastation. Grozny was first wrecked at the start of the last war in 1995. In the years since, residents patched up their apartment buildings with little outside help. Now, a three-month bombardment by Russian aircraft and artillery has destroyed the city once again. The remaining civilians are shocked and bewildered by what has happened to them, but Russian soldiers claim it as a triumph.

SOLDIER (translated): We have come here to stay. Not a single rebel bandit will ever live here again. We've put a stop to all that.

JULIAN MANYON: The Russians say they are still battling Chechen rebels in some outlying parts of Grozny. But in fact, it's now clear that about 5,000 rebels managed to break out of the Russian encirclement earlier this week. They took heavy casualties. Hundreds were killed or wounded in a mine field that the Russian army had laid across one of their escape routes. But the Russians have failed in their declared objective of trapping and destroying the main rebel force.