Demonstrators and police clashed in Hungary's capital, Budapest, on Monday - the 50th anniversary of the country's revolt against Soviet rule.
BBC correspondent Nick Thorpe explains the motives behind the protests and what impact the event could have on the country.
Who are the protesters?
A mixed bunch, mostly on the right of the political spectrum, they include students, professional people like doctors, dentists and businessmen - the "respectable middle class" - but also some radical right-wing elements.
The protesters were demonstrating against the prime minister
What they have in common is a belief that Prime Minister Ferenc Gyurcsany insulted the country with his speech made on 26 May at a private party, which was first broadcast on 17 September and contained admissions that the government had lied to help secure re-election.
Most of the protesters would have voted for Fidesz, the main conservative party in Hungary, in the April elections.
The more radical would probably have voted for the two far-right parties, MIEP (Hungarian Justice and Life Party) and JOBBIK, neither of which won enough votes to enter the Hungarian parliament.
There are ecologists, opposing globalisation. And there are also persistent rumours of "agents provocateurs" in the protesters' midst, trying to discredit the movement with acts of wanton violence.
Why are they protesting?
They are protesting first and foremost against Mr Gyurcsany, but also against the current Socialist-Liberal government and its economic policies.
Even before the leaking of the speech, they were upset that Mr Gyurcsany, a former Young Communist leader, would be leading the country during the anniversary events of the 1956 anti-Soviet revolution.
Because of the prime minister's admission of "lying, morning and night" about the state of the economy in order to win re-election, they say the election victory itself was a cheat. In consequence, opposition leader Viktor Orban has described the government as "legal, but illegitimate".
Is the economy a factor in the protests?
Yes, and it looks set to play a growing role.
The protests began as a spontaneous eruption of anger against the "lying prime minister" with a mainly political agenda - to oust the PM and, if possible, his government.
That government has launched an austerity programme in the past months - the one the PM admitted to covering up, in order to win re-election.
It includes an increase in taxes, including the introduction of a property tax, fees for visits to the doctor, and for students at universities, large increases in gas prices, and other measures which aim to cut Hungary's big budget deficit - expected to reach 10% of GDP this year - to 3% by 2009.
The austerity package is forecast to cost average Hungarians the equivalent of up to one month's wages. As the package bites this winter, the protests may become more social and economic than political.
So why hasn't the prime minister resigned?
The prime minister is something of a loner, an ambitious outsider in his own party who rose to power in a coup in the summer of 2004.
Both he and his rather lacklustre predecessor, Peter Medgyessy, are millionaires.
Some in the Socialist Party dislike his personality, some oppose his policies as too pro-market.
But they tolerated, even liked him as long as he won elections for them.
He hasn't resigned now partly because he believes he is the only person able to push through the economic package, and partly because he feels he still has the full support of his Socialists, and of their junior coalition partners, the Free Democrats.
If that support were to weaken, he might resign.
That is part of the strategy of the conservative opposition party, Fidesz - to pressurise Mr Gyurcsany's party into withdrawing its support.
Is there any link to the events of 1956?
According to the participants in the protests, definitely.
They give a variety of reasons. One is that the current Socialist Party is the successor of the Hungarian Socialist Workers Party (HSWP) which crushed the revolution in November 1956 and even operates from its old headquarters in Republic Square in Budapest.
They also say that the peaceful revolution in 1989 did not go far enough in forcing Hungarians to come to terms with their past, and should have disqualified certain people from office.
The PM and his supporters counter that there is no link whatsoever with 1956, and that the protesters today are little more than nationalist hoodlums. They argue that the clear Socialist-Liberal victory in April's general election gives them a democratic mandate to govern for four years.
They also stress the gulf that separates them from the HSWP - their commitment to social democracy, and to democratic practices in general. The inner workings of the Socialists are indeed democratic by Hungarian standards.
What does this mean for Hungary and its position in the EU?
It does not look good. The EU has cautiously welcomed Mr Gyurcsany's package, largely because it is the only one on the table.
If he had resigned the day after the speech was made public, no doubt EU leaders would have expressed confidence in the stability of Hungarian democracy, and have waited either to hear of the continuation of the austerity package under another Socialist prime minister, or the formulation of alternative proposals.
Fidesz have proposed a radically different package, based on tax cuts rather than tax increases.
The situation now is stalemate - Mr Gyurcsany refuses to leave, the protesters say they will stay on the streets until he goes.