By Gabriel Gatehouse
BBC News Kiev correspondent
No sooner had the two former Orange Revolution allies agreed on a coalition in December, than it started to fall apart.
The pair's rivalry has overwhelmed their alliance of convenience
Any notion of co-operation, or even civility between the two rivals, has long since vanished.
After months of bitter recriminations, Ukrainian Prime Minister Yulia Tymoshenko gave her blunt assessment of Viktor Yushchenko's actions as president: "A dictatorship of stupidity, irresponsibility and chaos."
The president was equally strident, accusing his prime minister of "high treason" for allegedly siding with Moscow over the conflict in Georgia - a charge she denies.
Indeed, the conflict in Georgia appears to have been the trigger for Ukraine's political realignment, earlier this month.
Firstly, the prime minister's faction blocked a motion condemning Russia's recent actions in South Ossetia and Abkhazia.
Then her MPs sided with the opposition Party of the Regions, to vote to curb the powers of the president.
This was too much for the members of the pro-presidential Our Ukraine party, and they left the chamber in protest.#
Later they announced they were quitting the coalition - which had been teetering on the brink of collapse ever since it was formed at the beginning of the year.
Viktor Yushchenko accused his rival of a constitutional coup, and threatened to call snap elections.
Now, the Speaker of the Parliament, Arseny Yatsenyuk, has declared the coalition officially dead.
Yulia Tymoshenko will continue to function as prime minister, as the parties reposition themselves and attempt to form a new working alliance.
One possibility is that her party could form a government with the opposition Party of the Regions. Its leader, and its electorate, is much more hostile towards further integration with Nato than President Yushchenko.
If within 30 days no new coalition is formed, President Yushchenko can call fresh parliamentary elections. These could be held as early as 21 December.
But opinion polls suggest his popularity lags far behind that of Ms Tymoshenko's party, and indeed behind that of the Party of the Regions.
Relations between Mr Yushchenko and Ms Tymoshenko have never been easy. But tensions have heightened since Russia took military action in Georgia a month ago.
Mr Yushchenko has been staunch in his support for his Georgian counterpart, Mikhail Saakashvili. Early on in the conflict, he flew into Tbilisi to appear at a rally in support of Georgia.
Ms Tymoshenko has been less forthcoming with her opinions on the crisis. She has declined to condemn outright the decision by the Russian President Dmitry Medvedev, to recognise the independence of South Ossetia and Abkhazia.
This has led some in Ukraine to speculate that she may be looking for Moscow's support for a possible bid for the presidency when elections are held in early 2010.
The presence of Russian ships in the Crimea is a divisive issue
While many Ukrainians, especially in the east of the country, feel a strong bond with Russia, there is also a sense of unease after events in Georgia last month.
Some in Kiev fear that parts of their country could be next in Moscow's sights.
The Crimean peninsula is seen as particularly vulnerable. It has a large ethnic Russian population, and is home to the Russian Black Sea Fleet.
The Ukrainian president has made it clear he wants all Russian ships out by 2017, when the current agreement expires.
The Russians say they want to stay, and the issue has become one of the flashpoints in the increasingly fraught relations between Kiev and Moscow.
The current crisis, though, is mostly the result not of policy differences, but of years of pure political rivalry.
Ms Tymoshenko herself has not said whether she intends to stand for the presidency in 2010, although most analysts believe she will. But if she did, and polls remained as they are today, she would be the favourite to win.
Whatever happens now, the controversial, ideological question of Ukraine's Nato ambitions looks like it will take a back seat to more pragmatic concerns.