Fidesz has made much of its promises to break the grip of the Socialists' business networks.
Jobbik is not represented in parliament, but it co-operates with Fidesz in some localities.
Some opponents of the changes staged a protest at Fidesz party headquarters last week.
But the referendum has dashed hopes of more reforms, and Fidesz has the initiative.
But one lot of Magyar oligarchs has been replaced by another, who are allies of Fidesz.
His party, Fidesz, insists that the constitutional changes conform with Hungary's legal responsibilities as an EU member.
Everybody will have to take responsibility for what they have done, says Peter Szijjarto, Fidesz's chief of staff.
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She was the only person on the policy board who was not appointed by either Mr Orban or Fidesz.
Mr Schmitt's resignation comes at a sensitive time for the embattled Fidesz government.
Mr Bayer has organised three "peace marches" in support of the Fidesz government.
However, Fidesz ministers are also on record for attacking anti-Roma and anti-Semitic remarks.
Fidesz and its allies the Christian Democrats voted for, along with three independents.
Hungary's presidency was marred by criticism of Fidesz's new media law and constitution.
He served as an MEP for the ruling right-wing Fidesz party before being appointed president in the summer of 2010.
Fidesz's initial response was to defend the Garda's right of free association, and accuse Mr Gyurcsany of whipping up hysteria.
Fidesz promises to reduce taxes and the burdensome bureaucracy, and thus create a million new jobs over the next decade.
Hungary's parliament has adopted a package of constitutional changes proposed by the ruling Fidesz party which critics say undermine democracy.
This was a massive show of support for Mr Orban and his Fidesz government, the BBC's Nick Thorpe in Budapest reports.
BBC: Thousands of Hungarians rally to back embattled PM Orban
Andras Simor, the bank's governor, has survived repeated calls from Fidesz for his resignation (as well as a large salary cut).
Fidesz is proud to belong to their umbrella group, and the biggest political family within the EU, the European People's Party.
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Mr Orban has been able to push through changes because of the two-thirds majority that Fidesz and its allies enjoy in parliament.
Opposition politicians and civil-society activists hoping that the forthcoming EU presidency would bring outside pressure to bear on Fidesz have been disappointed.
Fidesz's poll ratings are almost 40%, against some 15% for the Socialists.
His Fidesz government passed some of the most restrictive media legislation in Europe - and presented your average journalist with the perfect story.
The leader of Fidesz, Hungary's centre-right party, won a stunning two-thirds majority in parliament on April 25th, taking 263 of the 386 seats.
Three out of four opinion polls published last week showed Fidesz leading, with 46-50% of the voters' support against 38-42% for the Socialists.
Budapest, home to a fifth of the population, gave Fidesz only four of the city's 32 individual constituencies, and those by narrow margins.
Viktor Orban, the prime minister, has lost a useful ally, but his replacement will be chosen by parliament, where Fidesz commands a two-thirds majority.
In its first serious piece of legislation, Hungary's new Fidesz centre-right government is giving the 2.5m-odd ethnic Magyars abroad the right to Hungarian passports.
Received wisdom has long held that the big guns of Fidesz and the Socialists would not fire on each other, for fear of retaliation.
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