Germany's far-right Alternative for Germany (AfD) won a record 44% in Saxony-Anhalt on Sunday, leaving a small party with seats that could determine whether it can lead the nation's first far-right state government since World War II. Why it matters: Germany rebuilt its democracy after Nazi rule with unusually strong safeguards against extremism. AfD's breakthrough shows those barriers aren't stopping Europe's far right from becoming dominant electoral forces. The latest: AfD more than doubled its 20.8% share in 2021, hitting its highest vote share ever in a state election and finishing ahead of the center-right CDU at 17%. BSW, the party that hasn't ruled out working with the AfD, barely cleared the 5% threshold parties need for parliamentary representation. Together, AfD and BSW would hold 43 seats, one more than a majority. BSW, a populist party, combines far-left economics with far-right migration policies and calls for closer ties to Russia. Yes, but: The arithmetic may not be enough. BSW co-chair Amira Mohamed Ali said Sunday the party would neither vote for AfD's Ulrich Siegmund nor CDU Premier Sven Schulze. Instead, she wants a nonpartisan premier who would govern with BSW and AfD. This would require support from AfD, but Siegmund rejected the idea. Siegmund suggested Sunday he may persuade some lawmakers to switch parties to help him secure a majority. Catch up quick: AfD has won the most votes once before, in 2024, but it has never governed. In 2024, it finished first in Thuringia, marking the first far-right victory since World War II, but other parties kept it out of government. Sunday's result is AfD's strongest. Flashback: Trump allies' support for the far-right party became a transatlantic flashpoint during Germany's 2025 federal election. Elon Musk boosted the AfD on X, saying "only the AfD can save Germany," and he appeared by video at an AfD campaign rally. Vice President JD Vance met with AfD's leader just before that election and told the Munich Security Conference there was "no room for firewalls," a reference to mainstream parties' stance against governing with the AfD. Between the lines: Saxony-Anhalt's intelligence service has classified the state AfD as a right-wing extremist organization. Siegmund, AfD's 35-year-old candidate for Saxony-Anhalt's premier, has drawn scrutiny over his treatment of Germany's Nazi past. At AfD events, an emcee has shouted "Sieg!" and supporters answered "Mund!" — splitting his surname into a call-and-response that the head of Germany's Central Council of Jews says evokes Nazi chants. Siegmund declined to call the Holocaust humanity's worst crime, saying he would not presume to rank all crimes. The big picture: Europe's far right is moving in sharply different directions. Hungary's Viktor Orbán lost power after 16 years this spring, yet Italy's Giorgia Meloni leads the country's longest-serving uninterrupted postwar government. In France, far-right National Rally leader Marine Le Pen is the early front-runner for the 2027 presidential election. Context: Germany's postwar system was built in the shadow of the Nazis' destruction of the democratic Weimar Republic. The 1949 Basic Law embraces the concept of a "militant democracy" to defend against movements that seek to abolish the constitutional order. What's inside: The AfD laid out a program for how it would use state power: Rewrite the mandate of the state intelligence service that investigated the party. Allow homeschooling, give the government greater control over which textbooks schools can use and end its public broadcasting agreement with neighboring states. Create a deportation task force. Require state-funded organizations to demonstrate a "patriotic basic attitude." What we're watching: German officials, including the defense minister, have floated limiting intelligence sharing over concerns about AfD's ties to Russia.