The far-right Alternative for Germany, or AfD, had a very successful night in two East German states on Sunday, with nearly a third of voters voting for the party, whose state chapters have been classified as “confirmed extremist” by German domestic intelligence.

But while a far-right party doing so well in two German states less than eight decades after the end of Nazi Germany is symbolically fraught, it will likely have only limited impact on Germany’s national politics. Although a record number of voters turned out on Sunday in the two states, only about 7 percent of all Germans were eligible to vote.

Nor is the AfD expected to find allies easily. All the other parties that won statehouse seats on Sunday have committed themselves to not collaborating with the far right, in a strategy that will further alienate far-right voters but that is intended to ensure democratic stability in government.

Still, the elections will have ripple effects that are hard to predict, not least on the success of a far-left party that did not exist last year. In Thuringia, the smaller of the two states, nearly half of the voters chose extremist parties, which will force parties to make difficult compromises in the coming weeks if their leaders are to create a stable, working government.

In Saxony, where the mainstream Christian Democratic Union, or C.D.U., came in first, things are slightly more straightforward, in part because Greens and Social Democrats could retain a role in a minority government.

Here are some takeaways from the election: