'NOT A NICE PROCESS'
Some other party leaders, particularly in the east, have prompted public outrage with their comments on the refugee crisis.
Alexander Gauland, a trained lawyer with a penchant for tweed jackets who leads the AfD in Brandenburg, has compared refugees to barbarians who invaded the Roman Empire and said Germany should not be "blackmailed by children's eyes".
And trained teacher Bjoern Hoecke, the AfD's leader in the eastern state of Thuringia, said evolution had given Europe and Africa two different "reproduction strategies", with the African one "aiming for the highest possible growth rate".
Political scientist Hajo Funke, an expert on the far-right, said the AfD contained radical right-wing members as well as people who did not see themselves that way.
"That's why the AfD is playing it both ways - showing 'we're moderate' and 'we're not' - so it has attracted two groups: people protesting as they're unhappy with government policy, especially on refugees, and others who get incited to unleash their resentment."
For Germans who find the likes of Gauland and Hoecke too extreme, more moderate voices have been presented.
Chief among them is Meuthen, a 54-year-old bespectacled economics professor and twice-married father-of-five who is Catholic and goes to church when he can.
A polished speaker, Meuthen responded with aplomb to questions on the details of Germany's constitution at a recent rally in Baden-Wuerttemberg, a wealthy southwestern state that is home to luxury carmakers Daimler and Porsche and where the AfD won 15.1 percent of the vote last weekend.
A regional government economics specialist turned university professor, he closely watched the euro zone crisis unfold and thought the rescue packages breached the EU's no-bailout clause.
Meuthen decided to join a party for the first time after watching the AfD's founder - also an economics professor - on television on the evening of the party's debut, and failed, federal election campaign in 2013.
He has since become the AfD's little-known co-chairman, overshadowed by his colleague Frauke Petry, who has suggested migrants entering Germany illegally should be shot if necessary.
It's difficult to imagine Meuthen saying such a thing. When he told Reuters about the need to deport economic refugees, he stressed that deportation was "not a nice process".
He added: "The people who are all coming to our country now are only doing what we would do in their situation so we mustn't blame them."