Given a graph G, a 2-tuple total dominating set is a vertex subset S such that every vertex has at least two neighbors in S. The cardinality of a minimum 2-tuple total dominating set is called the 2-tuple total domination number. In this paper, we determine the 2-tuple total domination numbers of Hm,n for m ∈ {3,5}, where Hm,n stands for a Harary graph of n vertices with degree parameter m.