How long could it take until the new state governments are in place?
That won't happen quickly. The parties have to take their time, not least because, under not unlikely circumstances, the Sahra Wagenknecht Alliance (BSW) could end up participating in the government: The BSW has not yet been as professionally set up as the other parties. It is a largely inexperienced group with little personal involvement, which is orchestrated by Ms Wagenknecht. This could be a challenge for the BSW itself, but also for potential partners, such as the CDU.
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What position does this put the CDU in particular, which is currently ranked just ahead of the AfD in Saxony and second after it in Thuringia?
The CDU is the anchor of stability in both federal states. They have sufficient flexibility to form a coalition with all other parties except the AfD or to work together with the Left Party in Thuringia. They need this, because the FDP no longer has any parliamentary significance in the bourgeois spectrum.
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So a coalition with the BSW is also possible?
The CDU has already signaled that it is fundamentally willing to talk. It is characterized by pragmatism and avoids ideological battles of principle. The CDU would rather govern than be in opposition – and therefore will probably not recognize new constellations.