In the battle being waged from a street corner here Wednesday, Russian soldiers were targeting a Chechen sniper in an apartment building in Grozny, Chechnya's besieged capital just 400 yards away.

First, a pair of Russian sharpshooters pivoted into an alley behind houses on each side to fire on the sniper's nest. Then a wide metal gate at the rear of the alley opened. Three troopers wheeled out a large, snub-nosed machine gun and fired several intense bursts at the target.

The machine gun rolled back, and out of the same gate rumbled a T-80 tank, which stopped abruptly at the head of the alley. "Cover your ears," advised Col. Evgenny Kubarin, in charge of this sector of the front. But the stocky officer didn't bother to follow his own advice.

The tank fired, and the boom shook rows of houses along the alley, rattling windows and the people behind them. "That will take another piece of the hide-out. We'll see whether it took the sniper, too," Kubarin said, retreating to his post inside a half-constructed house.

The Russian attack on Grozny, almost a week old, marks the most dramatic episode of Moscow's three-month-old ground offensive against Chechnya's separatist rebels. The capital has been bombed with few pauses, and deprived of electricity, gas and running water for four months.

The city is still beyond Russia's grasp, however, and three days of reporting in and around Grozny this week suggest that Russian authorities' frequent predictions of its quick capitulation seem optimistic. Unless the Russians launch a multi-pronged assault or the rebels suddenly depart, it could take many days, or even weeks, to claim the city.

In one sign of their frustration, the Russians now say they have conquered only sections of the Staropromyslovsky and Chernorechye districts and a few other neighborhoods--places they declared fully vanquished a few days ago.

In the current fighting, a Russian advance of a few hundred yards is a major event. This little town of Staraya Sunzha, which abuts northeastern Grozny, is a case in point. On Dec. 10, Russian forces stood 300 yards from the town. They say it was taken on Dec. 25, but even now occupy only half of it. Danger from snipers, mortars and rocket-propelled grenades keeps the Russian forces from moving closer to Grozny's city limits.

A few days ago, the battle for Grozny could be best described as a lopsided standoff. On one side, the Russians poured artillery on the capital all day from positions in and behind the tin-roofed houses in Staraya Sunzha's neighborhoods. On the other side, the lightly armed Chechen rebels moved furtively from building to building to pepper advancing Russian armor or exposed spotters and infantrymen.

As elsewhere, the Russian bombardment was aimed at clearing the northeast urban zone so that, at some point, motorized infantry could move in, then push deeper into the battered capital until resistance is crushed or the rebels withdraw.

Russian officers are clearly wary of suffering heavy casualties, as happened in an ill-fated New Year's Eve assault in 1994. "Sometimes doing things quickly is the slow way," said Kubarin, a veteran of the first Chechen war.

By Russian officers' accounts, the brunt of their work is being done at long range. The targets may even be out of sight. "Snipers hide behind screens. All that might be visible is a barrel and a sight," Kubarin said.

The Chechens say they have up to 5,000 fighters in the city, and vow to defend it--although leaders acknowledged that at some point the capital could fall. "Even if after a while the Russian army manages to conquer Grozny, the price it will have to pay for it will be very high," said Chechen President Aslan Maskhadov.

The slow pace of conquest prolongs the nightmare for thousands of civilians left in Grozny, who have endured four months of bombing. There is little doubt that rebel hide-outs include buildings where noncombatants are cowering in basements. Targeting a sniper may well mean smashing an occupied building. At one point, Kubarin received a report that rebels with a rocket-propelled grenade launcher were on the roof of a building in the "Micro-district," the neighborhood that touches Staraya Sunzha.

"Take eight men, a couple of RPG's and an armored vehicle and squeeze them out," Kubarin said. "Check with someone to see if there are civilians there," he added, glancing at visiting reporters.

He sat at a long table in the half-finished house sipping tea and locating potential targets on a detailed map. The room was cluttered with grenade launchers, telephones and field radios. Outside, the thud of artillery was almost constant, mixed with occasional sniper fire.

"How many teeth do they have?" Kubarin barked into a walkie-talkie, using slang as he inquired about the amount of weaponry that had been spotted. "Hit Panther 5."

Other quadrants were marked with various fauna and flora: zebra, camel, mule, pine, maple, sable, bear.

The troops, who were under Interior Ministry command, included Chechens loyal to Moscow.

At Kubarin's command post, two men stood with their hands against the wall. One was a suspected sniper. "He had been pestering our positions all night," said a Russian officer. A few minutes later, the men disappeared, their fates unknown.

An alarming radio report reached Staraya Sunzha: Rebels had exploded a tank of chlorine gas meant to poison the Russians. The Russians assert that the Chechens have laid tanks of toxic chemicals throughout the city to wipe out advancing troops. The alarm about the approaching cloud seemed not to radiate beyond the command bunker. No one outside was putting on a gas mask or scurrying for cover. A report soon came that the wind was pushing the cloud into Grozny.

Outside, refugees from Grozny, now sheltered in Staraya Sunzha, ventured out of houses. An elderly woman on crutches pleaded for outsiders to come and rescue civilians. "There are many cripples over there," she said.

Kamesha, a middle-aged school teacher, debated with Kubarin about whether so much shelling was necessary--a local version of the Western criticism that Russia's war on Chechnya is disproportionate. "There aren't more than 15 fighters in the Micro-district," she said. "Why bomb, bomb and bomb? Also, you fire from here right by our house and frighten us to death."

"It is their fault," Kubarin said, referring to the rebels. "They are using the civilians as shields. Anyway, people had time to come out."