Russian troops seized the last important town held by Chechen rebels on Friday, starting a new phase of the war in the breakaway southern republic.
The fall of the town, Shali, forces the rebels to retreat to the mountains, where it will be difficult for them to obtain supplies or force the Russians to withdraw from the plains below.
For the Russians, it will be tricky to chase an elusive enemy in rugged terrain, the kind of problem they faced in Afghanistan. The Chechens waged a long guerrilla war in the mountains against Russia in the 19th century.
But the Russians have air support, and many Chechens appear to be tired of the fighting and seem ready to make peace.