DONETSK, Ukraine » The silver-haired mayor of this raw mining city in eastern Ukraine had just delivered a pep talk to about 100 uniformed police officers, beseeching them to ensure law and order in these turbulent times of revolution, when a bearded man in dark glasses took the microphone.

"If we want peace," the man proclaimed, "we have to get ready for war!"

The mayor, Alexander Lukyanchenko, 67, shot back: "And tell me, just who are you planning to fight?"

The answer was muddled talk laced with nostalgia for Soviet days and the supposed specter of nationalists from western Ukraine ready to crush the Russian-speaking East.

But the exchange between the third-term mayor, dapper in a fine dark blue suit, and the rugged speaker, who identified himself as "commander" of a previously unknown group, the Eastern Front, exposed the jangled nerves in this city of 1 million and the tough task facing leaders who know they must keep workers’ pay, pensions and supplies flowing even as they feel their hold on power waning.

Hundreds of miles to the west, the mayor of Lviv, Andriy Sadovy, has the same worries as Lukyanchenko: keeping things calm when the political system has all but crumbled and the police are widely hated after 82 people, most of them protesters apparently shot by police snipers, were killed in Kiev last week.

But of the two cities’ mayors, Sadovy, 45, a political independent elected twice since 2006, seems to hold the better cards.

He certainly seems to be enjoying his moment in the sun, with a young, English-speaking news team posting his near-daily briefings on YouTube, and perhaps ogling national office.

He apparently has had no trouble in uniting those police officers who are still on the job with civilian volunteers to form a force of about 2,000 people who patrol the streets at night and handle traffic.

And Sadovy made time to mourn at least one of the 13 protesters from the Lviv region who were killed in Kiev, placing three red roses on the open coffin of a 28-year-old history lecturer at a memorial last weekend.

This week, Sadovy acted swiftly to proclaim Russian-language days in Lviv after the Ukrainian Parliament passed a widely criticized law that stripped Russian of its official status, infuriating Russian speakers in Ukraine. Slightly stooped, speaking Russian, Ukrainian and some English, the bespectacled Sadovy, a father of four sons, dispenses books showing the centuries of history in Lviv, a maze of cobbled streets, Baroque-era churches, palaces and fierce nationalism.

He is proud of his city’s cooperation with European bodies, and like many residents looks to now-gleaming Krakow, in nearby Poland, as the model for Lviv, where barely five decades of Soviet rule are still felt in the dilapidation of once-splendid Hapsburg facades, or the barracks-like apartment blocks on the outskirts.

When Sadovy and his fellow western Ukrainians learned in November that their now fugitive president, Viktor Yanukovych, had spurned an association agreement with the European Union, which they had watched inject funds into Poland that helped spur its renewal, they exploded in revolt. By late January, they had declared Lviv independent of central authority — "Free City of a Free People," as the slogan reads on the huge Ukrainian flag now hanging on the ancient Town Hall.

With Yanukovych’s flight from Ukraine last weekend, the revolt succeeded in disposing of the man most people — even here in his hometown, Donetsk — denounce as murderous and extremely corrupt. But Yanukovych’s departure has left a power vacuum, with quarreling leaders in Kiev taking power on a tidal wave of hurriedly passed laws and an economy reportedly edging closer to bankruptcy.

"More economics, less politics" was the only policy offered by Lukyanchenko in Donetsk on Tuesday after his session with the police.

While he asked the news media not to play up the appearance of the self-styled Eastern Front commander, a day earlier, the mayor had appeared at a meeting that featured hundreds of masked and menacing men armed with clubs. A fellow Yanukovych acolyte, the governor of the Donetsk region, Andrei V. Shishatsky, had been filmed earlier inviting the crowd to celebrate what in Lviv is certainly a reviled, long-forgotten feast: the Day of the Soviet Army.

The contrast in the two cities lies not just in the present, but also in their pasts. Lviv — Lvov in Russian, Lemberg in German — pitched for centuries between Polish, Hapsburg, Czarist, Nazi and Soviet rule before the Soviet Union collapsed and Ukraine, a country of 46 million, became independent in 1991. The Soviet Union was, in effect, an interlude, with the last nationalist fighters quashed only in the 1950s.

Donetsk, by contrast, was founded only in 1869, just an hour’s drive from Russia. It was set up under the czars and reputedly populated with thousands of prisoners released from Siberia to dig coal shafts here.

Its architecture is profoundly Soviet; a huge Lenin statue is now a rallying point for fuming residents, mostly elderly men, who vent about "fascists" from western Ukraine. Streets still bear names like "50 Years of the USSR," which would count as a relic even in Moscow.

Donetsk, however, provides about 25 percent of Ukraine’s hard currency earnings, according to Nikolai Zagoruyko, a local leader in Yanukovych’s Party of the Regions. And the city can point to at least one moment of recent revolt: 1989 and 1990, when hundreds of thousands of mineworkers went on strike and took to the streets.

"The miners then were the biggest force which moved the country," said Natalya Kuchar, 38, who works for the local independent trade union and whose father was one of the miners’ leaders.

One man who benefited from the strike was Rinat Akhmetov, a billionaire who has bought Donetsk a fine soccer team, built a splendid stadium that was a site for the European soccer championship in 2012 and, unlike Yanukovych, whose campaigns he has supported, has stayed on the job. Indeed, he is so busy, said a spokeswoman, that he had no time to meet foreign reporters making rare trips to Donetsk.

On Wednesday, Yanukovych sent a letter to the employees of his company, System Capital Management, said to number 300,000. Akhmetov, who appeared to back away from Yanukovych in recent weeks, wrote that "we, like all Ukrainians, are trying to found a new country in which democracy and the supremacy of law will be established, and the protection of property, free competition and social welfare provided." For that, according to a copy of the letter obtained by the newspaper Donskiye Novosti, extensive reforms are required.

How those changes are introduced is perhaps one secret Akhmetov is so far keeping to himself. Neither the fretting mayor, Lukyanchenko, nor the governor, Shishatsky, have offered much of a clue. Both have declared their loyalty to the still functioning Parliament in Kiev, and reiterated that Ukraine must hold together.

With rival television channels in Russian and Ukrainian offering wildly divergent versions of events, however, a split seems not unlikely. Kuchar, the union worker, said that her in-laws understood only the Russian broadcasts, and that when she and her husband gave their view of events, "they say things that make your hair stand on end."

As a result, she said, despite the couple’s relief at Yanukovych’s ouster, "we are very careful about being happy."

Alison Smale, New York Times

© 2014 The New York Times Company