It's the last test of German public opinion before September's national election -- and of the popularity of the far right.
The eastern German state of Saxony-Anhalt heads to local polls on Sunday (June 6).
Surveys in the state show a small lead for Chancellor Angela Merkel's party, the Christian Democrats - or the CDU.
But the far-right Alternative for Germany - or AfD- was running just one percentage point behind in the final poll published on Friday.
A loss or a tight margin of victory for the CDU could be a blow for party leader Armin Laschet's hopes of succeeding Merkel.
The conservative Saxony-Anhalt premier Reiner Haseloff said he had done all he could to persuade voters not to turn to the far right.
Meanwhile, AfD frontrunner Oliver Kirchner said he hopes Sunday's result will be, quote, "trend-setting" for the national election.
Merkel, who has been in power since 2005, is stepping down after the federal election.
Senior CDU officials concede that it will be tough to retain their party's appeal to voters when she's gone.