The east German state of Thuringia found itself facing a political stalemate on Sunday after elections failed to produce a majority for any discernible governing coalition, in a result that highlights how fragmented Germany's political landscape has become.

According to projections by Germany's MDR news channel, the elections were won by Die Linke, a hard-left party with its roots in the East German communist party, which garnered 31 per cent of the vote. But despite its strong performance it is unclear how Die Linke will be able to cobble together a functioning coalition government.

The party currently rules Thuringia in an alliance with the left-of-centre Social Democrats and the Greens. But after Sunday's election, the so-called red-red-green coalition will no longer command a majority in the regional parliament. The SPD won just 8.2 per cent of the vote, the Greens 5.1 per cent.

Angela Merkel's Christian Democratic Union, which came third, with 21.6 per cent of the vote, has refused to co-operate with Die Linke. The liberal Free Democrats (FDP) were on 5 per cent.

The big winner of the election was the Alternative for Germany, a far-right, anti-immigration party, which saw its share of the vote increase from 10.6 per cent in the last Thuringian elections in 2014 to 23.8 per cent.

That represents a big win for the party's leader in Thuringia, Björn Höcke, a nationalist firebrand and former history teacher who is one of Germany's most controversial politicians.

Mr Höcke's success will strengthen the "Wing", the hard-right faction of the AfD that he leads, and could exacerbate already deep-seated tensions between hardliners and moderates in the party.

While "red-red-green" will no longer command a majority, it could if Die Linke succeeds in persuading the FDP to join the government. It would be Germany's first such four-party coalition since reunification.

The CDU had hoped to be able to form a "coalition of the centre" with the SPD, FDP and the Greens - an alliance nicknamed Zimbabwe in Germany, because the colours of the four parties correspond to those of the Zimbabwean flag. Yet even such an unwieldy coalition would not have a majority of seats, according to MDR's projections.

Under the Thuringian constitution, the Linke prime minister of Thuringia, Bodo Ramelow, can theoretically stay in power in a caretaker capacity, as head of a minority government.

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The Thuringian election cements the AfD's role as the big opposition party in the east. In September, it won 27.5 per cent of the vote in the eastern state of Saxony and 23.5 per cent in Brandenburg, becoming the second-strongest party in the regional parliaments of both states.

Taken together, hard-right and hard-left parties won 53.5 per cent of the vote in Thuringia, a result that will ring alarm bells in Germany's corridors of power just as the nation prepares to mark the 30th anniversary of the fall of the Berlin Wall.

Die Linke and the AfD have been able to harness widespread dissatisfaction in the East, where the collapse of once state-owned industries after reunification led to high unemployment and social hardship. A recent survey found almost 60 per cent of residents in the east felt they are treated as second-class citizens, and more than half said German reunification was not a success.

That is despite a gradual process of economic convergence that has seen a marked improvement in living standards in the eastern states over the past couple of decades. Average salaries in the east are now at 86 per cent of the level in the west, and unemployment there has fallen sharply, from 18.7 per cent in 2005 to 6.9 per cent last year.

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