Polls opened at 8:00 am in the eastern German city of Dresden, where voters are casting the last ballots in the country's inconclusive national election.
There are about 219,000 eligible voters in the district, where the September 18 general election was postponed due to the death of a local candidate.
Angela Merkel's conservatives won three seats more than Chancellor Gerhard Schroeder's Social Democrats in last month's national vote, but neither side won a majority in the 613-seat parliament.
Even though the outcome in Dresden is not expected to change the preliminary September 18 result significantly, Germany's voting system means Schroeder's SPD could gain a seat or two and strengthen his hand in negotiations with Merkel.
The hung parliament has pushed the two main parties to explore joining forces in a "grand coalition" and financial markets have warmed to the prospect, believing it well suited to mastering the country's various economic woes. Share prices have climbed to 3-1/2 year highs this week.
But the negotiations could take months and may never get off the ground because both Merkel and Schroeder are insisting they should lead the next government. The CDU and SPD could, in theory, form separate three-way alliances with smaller parties.
Because of Germany's complex system, the Dresden vote could wipe out the CDU's parliament lead only if the SPD wins 140,000 votes more than the CDU. The district has only 219,000 voters and a 140,000-vote margin of victory is seen as virtually impossible.
That has not stopped both Schroeder and Merkel from campaigning in the district in Dresden, 200 km south of Berlin. The rest of the 299 districts voted two weeks ago.
Schroeder and Merkel attacked each other as unqualified to lead Germany at separate campaign rallies in Dresden on Friday.
Both the CDU and SPD are hoping for a strong result in Dresden on Sunday for a psychological boost to reinforce their negotiating positions in forging a "grand coalition" to implement vital economic reforms