On his recent visit here, President Obama mistakenly referred to Russia's No. 2 as "President Putin."

He brushed it off, noting that Prime Minister Vladimir Putin formerly held the country's top post – which he did, before paving the way for protégé Dmitry Medvedev's election in March last year.

If Putin's title trips up a world leader here and there, pinpointing his exact role confounds nearly everyone.

Amid the worst economic bad news in over a decade, the question of just how Russia is being led – and where – has become the subject of heated debate among the country's political class.

Some experts say it's a stage-managed Kremlin theater production, a "good cop, bad cop" act designed to keep the opposition off-guard and the public guessing.

Others suggest that President Medvedev, a savvy lawyer fond of Led Zeppelin, may be breaking away from the tutelage of his predecessor and challenging the harsher aspects of the Putin era.

A May poll by the independent Levada Center in Moscow found that 19 percent of Russians believe that Medvedev "pursues an independent policy," while 68 percent think he acts entirely "under the control of Putin and [his] entourage."

That street wisdom reflects the past thousand years of Russian history, in which the country has always been ruled by a single strong leader. Rare moments of divided authority have usually been times of threatened civil war, most recently in 1993 when gridlock between President Boris Yeltsin and his elected parliament culminated in gunfire and the subsequent restoration of near-total Kremlin power.

Hence the widespread skepticism last year when Medvedev was vaulted into the Kremlin in a controlled election and Putin moved offices but kept the spotlight he had previously enjoyed.

'Medvedev is a general with no army'

Under Russia's 1993 Constitution, the prime minister is an appointed technocrat who serves at the president's pleasure. In the past, most have toiled in the Kremlin's shadow. But Putin's daily activities have been covered by Russian state TV as fully as Medvedev's. At times of emergency – such as the recent war with neighboring Georgia – Putin has taken center stage.

Both men have repeatedly insisted that their "tandem" is working well. So far, events have borne out that claim.

Olga Kryshtanovskaya, one of Russia's top experts on its political elite, says that if one ignores the terms of Russia's Constitution and looks at who actually holds the levers of power, the apparently peaceful relationship makes sense.

"Medvedev has no resources and no team to lead; 85 percent of all key posts are held by Putin's people. Medvedev's a general with no army," she says. "The plenary powers of the leaders have been distributed without any reference to the Constitution. Medvedev might chair sessions of the Security Council, but Putin actually controls the siloviki," meaning the military and security services.

In a burst of assertive activity recently, Medvedev has reached out to Russia's liberals, who were squeezed out of parliament, virtually banned from mainstream media, and shoved to society's margins under Putin.

In April, Medvedev gave a major interview to the Kremlin's longtime nemesis in journalism, the crusading weekly Novaya Gazeta. He introduced a presidential blog and ordered experts to draw up revisions to the Putin-era law on nongovernmental organizations, which civic leaders have decried as a straitjacket on political activity. He also met with leaders of small parties unable to win representation in the Duma in recent elections, and pledged to ease Putin-era restrictions.

Why Putin is throwing pens on national TV

Critics deride these moves as symbolic, but some say they may be an attempt to consolidate support as Medvedev prepares to assert himself as Russia's legitimate leader.

"Putin still believes that he is the No. 1 person in the country, but the problem is that Medvedev is beginning to think much the same of himself," Dmitry Oreshkin, head of the Mercator Group think tank in Moscow, told Ekho Moskvi radio recently. "Putin is more and more obviously taking up a tough, authoritarian position, as if he knows he is being pushed from power and is showing that he will mount fierce resistance."

Earlier this month, Putin rushed to the scene of a workers' strike in western Russia, where he angrily threw a pen at a wealthy tycoon – on national TV – and ordered all the workers' demands to be met. In another odd piece of political theater, Putin angrily upbraided the entire cabinet in a televised July government meeting.

Experts say the truth will probably not be revealed before presidential elections in 2012. Late last year, Medvedev pushed through controversial amendments to Russia's Constitution that extend presidential terms to six years.

"Of course this division of power cannot work as an institution in Russia; this is just a unique situation," says Alexei Push­kov, a member of the Kremlin's Council on Human Rights. "We'll know what's really going on when we see which of them will be running for president next time. Then it will totally become clear," he says.