The "Marriage for All" bill was backed by President Francois Hollande's Socialists and other left-wing MPs.
Mr Yanukovych has built a majority in parliament, with the help of communists and socialists.
Fidesz has made much of its promises to break the grip of the Socialists' business networks.
To general surprise, the Socialists accepted his resignation and produced two candidates for the succession.
With the Socialists now on board, he may instead bring it forward, possibly to next May.
ECONOMIST: Members of the Socialist Party vote for the EU constitution
Last year the Socialists agreed to abstain on what was also a contentious austerity budget vote.
Opposition socialists say this is proof that Sarkozy's tough security measures have been a failure.
Nobody doubts she will succeed: the Socialists grabbed 49% of the vote in Lille in 1995.
But will anyone else want to lead Spain's Socialists into what looks like certain defeat?
The ruling Socialists in Portugal saw their vote fall sharply, allowing the centre-right to claim victory.
The parliamentary opposition also took in Christian Democrats and Socialists from various other European countries.
The federalist notions of Pasqual Maragall, leader of its local Socialists, would mean big constitutional changes.
As the left elsewhere in Europe modernises, the radical shift of France's Socialists looks odd.
Such talk has delighted European socialists, who have found unlikely common cause with the centre-right president.
The Socialists called on other parties to also come clean when hit by scandals.
Mr Arnault applied for a Belgian passport soon after the Socialists won elections last year.
FORBES: Bernard Arnault Hops It To Belgium: And Just What Is A Fair Rate Of Tax Anyway?
PS's programme when, like left-wing parties all over Europe, the Socialists have moved to the right.
He has an absolute majority in parliament and leads the opposition Socialists in the polls.
Whereas the right used to be reticent and the Socialists keen, things have come full circle.
The ruling Socialists want this vote to pass, whereas their centreright opponents hope it will fail.
Some Albanians worry that the Socialists are a bit too popular in mafia-run places like Vlore.
French Socialists dreamt up the idea but are suddenly talking of new conditions for joining.
Polls put the Socialists ahead, though their lead varies (some say it is only 1.4 points).
French-speakers in the south plumped for Socialists, who want to keep the country together.
The French Socialists will also now tax investment income at the same high rates as regular income.
The opposition Socialists have a strong lead after the first round of the cantonal elections, on 25%.
The nationalists they threw out of power were junior partners in a coalition led by local Socialists.
After eight years of sloth and corruption under the Socialists, Hungary's economy is in a parlous state.
When Mr Delors declined in 1994 to stand for the presidency, many Socialists turned to Mrs Aubry.
Yet Spain's two big parties, the People's Party and the Socialists, devolve few decisions to their members.
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