The Chechen guerrilla units are being pushed back but not defeated. The mountains of southern Chechnya are still unconquered. The capture of Grozny will be only a symbolic victory as the city has been a pile of ruins since the last war.
At the same time, Russia has suffered no humiliating defeats. Its casualties have increased in the last week as its troops fight more on the ground, rather than relying on artillery and air power, but its losses are sustainable. A problem for the Russian army is that its grip on the central plains of Chechnya is more fragile than it looks. In at least two villages in western Chechnya, nominally under Russian control, the guerrillas feel secure enough to keep Russian prisoners of war.
The Russian campaign, now in its third month, has never had a clear objective in Chechnya. Vladimir Putin, the Russian Prime Minister, says his aim is to get the Chechens to hand over "terrorists". He has never explained how he expects that to be done.
The aim of the war in terms of Russian politics is clearer. It is to ensure that Mr Putin succeeds Boris Yeltsin as President in the election next June. So far it has succeeded. Opponents of Mr Putin, who were riding high in August, have fallen silent, fearful of being portrayed as unpatriotic.
Will Mr Putin be able to play the patriotic card for the next six months? It looks doubtful. He needs a short, victorious war. But the tactic of keeping Russian casualties low by relying on superior firepower means that Chechen guerrillas simply retreat and can always counter-attack. They suffer few losses, despite the Russian military's extravagant claims. In one village local people said that Russian shelling killed three cows and wounded a cowherd; a few hours later Russian radio reported that 70 Chechen fighters had died.
The tactic of relying on a First-World-War-style bombardment, which hits mainly civilians, holds another disadvantage for Russia. At the start of this war ordinary Chechens were disillusioned with their attempt to create a de facto state in the three years since their victory in the 1994-1996 war.
One Chechen who fought in the last war said he would not fight in this one. "Then, I fought for a Chechen state, our people and the Muslim faith," he said. "Instead we got a bandit state, our people were reduced to economic misery and our faith was split between traditional believers and the Wahhabis [Islamic extremists]."
The savagery of the Russian onslaught has left little opportunity for those Chechens who want an accommodation with Moscow to have any influence. The brutality of the Russian occupation means that villages that want to stay neutral end up supporting the guerrillas. The Kremlin is facing a long war, which will not be in its interest come next year's election.
More immediately, the upsurge in ground fighting and the threat to kill everybody in Grozny is probably a sign that the Russian generals are under pressure to finish the war. It has taken them almost three months to conquer half of a country the size of Yorkshire.
There is a hint of desperation in the Russian ultimatum to civilians in Grozny. In fact it was wholly counter-productive. It crystallised international opposition without noticeably frightening the Chechens, who point out that Russian artillery and aircraft are already pounding the city. Once again Moscow is discovering that it is easier to start a war in Chechnya than to finish it.