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The main result of this paper is that the outer automorphism group of a freeproduct of finite groups and cyclic groups is semistable at infinity (providedit is one ended) or semistable at each end. In a previous paper, we showed thatthe group of outer automorphisms of the free product of two nontrivial finitegroups with an infinite cyclic group has infinitely many ends, despite being ofvirtual cohomological dimension two. We also prove that aside from thisexception, having virtual cohomological dimension at least two implies theouter automorphism group of a free product of finite and cyclic groups is oneended. As a corollary, the outer automorphism groups of the free product offour finite groups or the free product of a single finite group with a freegroup of rank two are virtual duality groups of dimension two, in contrast withthe above example. Our proof is inspired by methods of Vogtmann, applied to acomplex first studied in another guise by Krsti\'c and Vogtmann.

One-endedness of outer automorphism groups of free products of finite and cyclic groups