Few polling places for today's parliamentary vote were situated at a more poignant site than the one on Kashirskoye Road in south Moscow. Next to a school where the ballots were cast is an open lot marked by an iron monument to the dead at what used to be No. 6, House 3.

The apartment building there was blown up in September, one of two destroyed by terrorist blasts in the capital, along with two others in provincial towns. In all, nearly 300 people died in the explosions, about 120 on Kashirskoye Road alone.

The explosions--which Russian authorities, without producing evidence or suspects, have blamed on Chechen separatist guerrillas--changed the course of Russian politics, providing a powerful rationale for the Russian military's offensive in Chechnya. That event, in turn, has sharply boosted the popularity of Prime Minister Vladimir Putin and the Unity party he backed in today's vote.

It is not certain how far the Chechen war can carry Putin--an obscure security official just four months ago and now a leading candidate to succeed President Boris Yeltsin in next summer's election--or the Unity party, but one thing was clear from conversations today with Moscow voters: The search for a strong hand to guide Russia is much on their minds.

"I believe that the bloc I voted for will best destroy the bandits who did this," said policeman Viktor Bessonov, gesturing to the monument and employing the government's derisive term for the Chechen rebels. He cast his ballot for Unity.

"The state is the state, and it must be protected," said Galina Garus, a retiree who voted for the Fatherland-All Russia list of candidates headed by former prime minister Yevgeny Primakov and Moscow Mayor Yuri Luzhkov.

"They're beasts," World War II veteran Vladimir Sokolinsky said of the Chechens, as he showed off a billboard of medals on his chest before entering a voting booth. "No talks with Chechens, no compromise; they're worse than the fascists," Sokolinsky said." His ballot went to the Communists.

Russians largely have been shielded from bad news in Chechnya--a region of the northern Caucasus about 1,000 miles south of Moscow--so negative events there were unlikely to affect today's balloting. Even the reported deaths of more than 100 soldiers last week during an apparent army incursion into Grozny, the Chechen capital, made news for only a day in the Russian media; no television or newspaper outlet probed the reports closely. In general, the media have been supportive of the offensive.

In Chechnya today, Russian forces heavily shelled Grozny, and battles were reported at the city's edge, as military chief of staff Gen. Anatoly Kvashnin, gave the Interfax news agency an upbeat assessment of the situation there. He asserted that the army is in complete control of the flatlands of northern and central Chechnya and has begun to penetrate the mountainous south. He did not claim army control of any part of Grozny.

Russian authorities have been in communication with representatives of Chechen President Aslan Maskhadov, Kvashnin said, but only to reiterate long-standing conditions for halting the offensive: The Chechens must surrender and hand over "terrorists."

Russian voters, apparently united on the need for strong leadership and for crushing Chechen separatism, were also in agreement that the economy needs improvement, but some split over a generational issue.

Those who believe governmental experience is important seemed to favor the Fatherland-All Russia slate. Primakov, 70, was a Soviet-era bureaucrat, foreign intelligence chief under Mikhail Gorbachev and foreign minister under Yeltsin before serving as prime minister for nine months. Luzhkov, 63, has been involved in Moscow city politics for years and has been mayor since 1992. Those who believe veteran leaders cannot cope with current problems mentioned Unity or the Union of Right Forces, both of which feature younger leaders.

"The old don't bother me so much, if they have performed," said Yuri Surinov, a Luzhkov backer who described his profession as, "Let's just say commerce." Said Andrei Shaposhnik, a policeman: "We need serious, active people. Putin fits that description."

The capital was calm as the voting proceeded. By evening, the only untoward incident proved to have comic overtones. Police examining a suspicious bag left in front of Communist Party headquarters discovered not bombs, but two dozen bottles of vodka. Communist representatives complained that someone had placed the liquor there to associate Communists with ballot-day bribery--offering vodka for votes. "We have nothing to do with this provocation," Communist spokesman Anton Vasilchenko said soberly.