GROZNY -- A Russian armored personnel carrier strayed into Chechen-controlled southern Grozny on Monday, racing along the main road through a Chechen checkpoint and heading east.


When it reached the village of Alkhan-Kala, just outside the city, the APC fired its canon. People at the roadside market and small boys selling cans of gasoline ran for cover. Cars swerved off the road.


And a blue Zhiguli took off in hot pursuit.


Roaring down the road, its lights on high-beam and weaving through oncoming cars, the Zhiguli overtook the Russian armored vehicle, just beating it to a roadblock.


Leaping out as the car skidded to a halt, four Chechen fighters took up positions behind broad concrete blocks at the checkpoint, machine guns and anti-tank rockets at the ready.


They caught the APC as it came through, blowing out tires on one side. The Russians kept going another kilometer before turning down a track. They abandoned the APC by some trees and ran off into the woods, the Chechens still in pursuit. Gunfire continued to crackle across the field half an hour later.


What the Russians were doing on the road was not clear. Locals suggested they had come from the Russian-held village of Yermolovka. One Chechen fighter said the Russians had to be drunk to do something so senseless.


The Chechens climbed atop the vehicle, inspecting their "trophy," elated with another small victory -- another David and Goliath episode in a war often fought between Kalshnikov and tank.


Closer to the center of Grozny, spirits among the Chechen fighters were high despite news that Russian tanks were inching closer to the presidential palace.


"Tanks are all around the palace firing from all directions. Our fighters are fighting on both sides of the palace. They are going around behind the building to attack the Russian forces," said Lieutenant Colonel Ali Makhayev, a white-bearded, burly Chechen, in combat fatigues and a helmet trimmed with a green Islamic ribbon.


Sultan Nuri, 57, deputy chairman of the committee in memory of the 1944 genocide of the Chechen people, said he had managed to reach the presidential palace at noon.


In a long, dark gray overcoat, he shrugged off the danger of shelling and snipers.


"I was deported at the age of five. That was a worse experience than now," he said. "They deceived us then, they sent us like cattle, and we had no arms, no way of defending ourselves. This is far easier. We are fighting for freedom, we have arms in our hands, and have a running chance of winning."


Fighters came striding up the hill from the center of town, smiling and laughing, big packs of cola on their shoulders. They handed cans out, a present from a shopkeeper whose store had been wrecked.


One lucky recipient was a six-year-old girl, skipping in the courtyard with her friend. Pale-faced and thin, she and her mother, Taisiyeva Chernova, 41, were living along with one other family. Their apartment block is just behind Lenin Street, the scene of some of the most vicious shelling over the past three days.


"I am afraid, but I decided to stay," said Chernova, an ethnic Russian, a single mother and former construction worker. "Life was so good here. It would be sad to leave, and I have a nice apartment," she said as she pointed out her second-floor windows, remarkably still intact.


"The intelligentsia all left -- people with money," she said. "Those who remain are the ones who are too old or too poor to go." She and her daughter sleep in the kitchen, where the cooker provides some warmth. Only when the shelling was very heavy did they go to the basement.


Chernova's reluctance to leave her home was echoed by a convoy of Chechen refugees returning home to the village Dolinsky, northwest of Grozny, the scene of a fierce battle in December.


As the Russian army advanced on Grozny the refugees fled south to the village of Urus-Marten. Seventy refugees live together there in a school.


"The people there are having difficulty living, and it is even more difficult for them to help us," said one woman standing in the back of an open truck filled with 30 men, women and children. After a month, it was time to go home, she said.


Magomed Musayev, 44, the leader of the convoy, expressed concern about the attitudes of the Russian soldiers who control Dolinsky, "There is half a chance of danger, but we feel anxiety not being at home, we want to go back. We are peaceful people, and we think they will understand that."


They set off heading north against the darkened sky, blackened by at least 10 fires burning at the oil refinery east of Grozny.