It is well-known that there exist groups which cannot be realized as full automorphism group of any group, obvious examples being the (non-trivial) cyclic groups of odd order and (non-trivial) free groups. It was proved by \textit{D. J. S. Robinson} [Q. J. Math., Oxf. II. Ser. 30, 351-364 (1979; Zbl 0418.20031)] that also infinite Chernikov groups cannot occur as full automorphism groups. It was more recently shown by \textit{A. Russo} and the reviewer [Ric. Mat. 51, No. 2, 337-339 (2002; Zbl 1144.20309)] that the only group admitting the infinite dihedral group \(D_\infty\) as full automorphism group is \(D_\infty\) itself. In the paper under review, the authors prove that the automorphism group of a group \(G\) is an infinite locally dihedral group if and only if \(G=\langle x\rangle\ltimes A\), where \(A\) is a torsion-free group of rank \(1\) and finite type at each prime, and \(x\) is an element of order \(2\) inverting all elements of \(A\). Moreover, in this situation \(G\) is isomorphic to its automorphism group.