Let G = (V, A) be a digraph. A set T of vertices of G is a twin dominating set of G if for every vertex v ∈ V T. There exist u, ω∈ T (possibly u = ω) such that (u, v), (v, ω) ∈ A. The twin domination number γ*(G) of G is the cardinality of a minimum twin dominating set of G. In this paper we consider the twin domination number in generalized Kautz digraphs GK (n, d). In these digraphs, we establish bounds on the twin domination number and give a sufficient condition for the twin domination number attaining the lower bound. We give the exact values of the twin domination numbers by constructing minimum twin dominating sets for some special generalized Kautz digraphs.