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Automorphic loops are loops in which all inner mappings are automorphisms. We study a generalization of the dihedral construction for groups. Namely, if $(G,+)$ is an abelian group, $m\ge 1$ and $\alpha \in Aut\left(G\right)$, let $Dih(m,G,\alpha )$ be defined on ${\mathbb{Z}}_m\times G$ by $$(i,u)(j,v)=(i\oplus j,({(-1)}^{j}u+v){\alpha }^{ij}).$$ The resulting loop is automorphic if and only if $m=2$ or (${\alpha }^2=1$ and $m$ is even). The case $m=2$ was introduced by Kinyon, Kunen, Phillips, and Vojtěchovský. We present several structural results about the automorphic dihedral loops in both cases.