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According to the trend results, the CDU remained the strongest party in the local elections in Hesse.
It came nationwide to 28.2 percent of the vote, as the State Statistical Office announced on Monday in Wiesbaden on its website.
It is followed by the SPD with 23.3 percent, ahead of the Greens with 19.4 percent.
According to the trend, the AfD came to 8.1 percent, the FDP to 6.6 percent and the Left to 4.1 percent.
In the local elections in 2016, the CDU in Hesse became the strongest force nationwide, with 28.9 percent.
The SPD had 28.5 percent of the vote, the AfD 11.9 percent.
The Greens ranked 11.3, the FDP 6.4 and Die Linke und Linke List 4.5 percent.
New district assemblies, city and community parliaments and local councils were elected on Sunday.
In the days before the vote, there was already a high number of postal votes.
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The turnout was 50.4 percent - after 48 percent in the election five years ago.
The city council elections in the independent cities and the district elections flow into the nationwide figures.
According to the State Statistical Office, the trend result is an interim result and only shows part of the votes counted: only the ballot papers for which an election proposal was accepted without change are taken into account.
The ballot papers without a list cross are not included in the trend result.
Throughout Hesse, around 4.7 million men and women were eligible to vote on Sunday - including 423,000 EU foreigners.
Candidates from a total of 20 parties and 585 groups of voters threw their hats into the ring for a place in the local parliaments.