Germany’s anti-immigration party Alternative for Germany is on course for victory in the eastern state of Thuringia, according to an exit poll.

The AfD is set to win 30.5% of the vote, says the exit poll for public broadcaster ARD, six points ahead of the conservative CDU, and far in front of Germany’s three governing parties.

If confirmed, it would give the far right its first vote win in a state parliament since World War Two, although it is unlikely to be able to form a government in Thuringia.

Some five million Germans were eligible to vote in two state elections in the east on Sunday. The AfD is also close behind the conservative CDU in the election for a state parliament in Saxony.

The ARD exit poll gives the CDU 31.5% and the AfD 30% in Saxony, again far ahead of the three parties running the national government.

The AfD’s top candidate in Thuringia, Björn Höcke, is a highly controversial figure in Germany.

His party has been designated as right-wing extremist and he has been fined for using a Nazi slogan, although the former history teacher denies knowingly doing so.