The ditty pokes fun at the power-play between the two men
Dmitry Medvedev and Vladimir Putin have been gently lampooned in a new year's cartoon broadcast on Russian TV.
Animated figures of Russia's president and prime minister are shown dancing in Moscow's Red Square and singing a duet about 2009.
President Medvedev is depicted playing an accordion while Mr Putin beats a tambourine against his bottom.
Channel One television broadcast the cartoon after Mr Medvedev's official new year address.
The ditty was featured in a special episode of Mult Lichnosti (a play on the Russian for "cult of personality") - a biweekly show poking fun at public figures.
The two-and-a-half-minute cartoon, with surprisingly true-to-life voices, has surprised Russians used to serious depictions of their leaders.
The duet jauntily refers to events in the past year, such as the failed attempt by a consortium including Russian bank Sberbank to buy Opel from General Motors, and the construction of Russia's Nord Stream gas pipeline.
With fireworks exploding above the Moscow skyline in the background, Mr Medvedev's character performs a dainty leap for which he is congratulated by the prime minister, who is then lauded for his own little jump.
By Richard Galpin, BBC News, Moscow
For those of us who follow political developments here, what is most surprising - if not shocking - about this very tame piece of satire is that it appeared on the biggest state-controlled channel.
It speaks volumes about how effectively the broadcast media has been muzzled since Vladimir Putin rose to power 10 years ago.
In the previous decade, under ex-President Boris Yeltsin, there was a brief renaissance when the media was free to publish or broadcast bitingly-critical items about the country's leaders.
But those days are long gone, particularly for the main TV and radio stations which have the greatest influence over the population given their nationwide reach.
Channel One leads the way as a mouthpiece for the government, with its bulletins filled with long-winded Soviet-style reports about the day-to day activities of Prime Minister Putin and President Medvedev.
So this cartoon does represent something new in the current, carefully-controlled political environment.
Their ditty gently mocks the power-play between them since Mr Medvedev took over the Russian presidency from Mr Putin in 2008.
"I just did my second New Year's greeting to the nation," says Mr Medvedev proudly at one stage, to which Mr Putin replies: "I've done it nine times, you know."
They poke fun at the EU and US, International Olympic Committee president Jacques Rogge, Ukraine's President Viktor Yushchenko and even make a reference to historic corruption within Russia's bureaucracy.
Konstantin Ernst, Channel One's director, said the Russian leaders were being added to the regular cast of Mult Lichnosti, the New York Times reported.
"We have to be careful," he told the newspaper. "You can insult someone in show business, because a person like that is selling himself, and does not answer for anything else.
"Whereas the president and prime minister also represent the work they do."
Mult Lichnosti also features other world leaders. One episode of the cartoon shows Ukraine's President Viktor Yushchenko inflating balloons with natural gas diverted from a Russian pipeline.
Georgia's President Mikhail Saakashvili is seen eating his own tie.
And US President Barack Obama is depicted endlessly bouncing a basketball up and down.