Let A be a nontrivial abelian group. A connected simple graph G = (V, E) is A-antimagic, if there exists an edge labeling f : E(G) → A\{0 A } such that the induced vertex labeling f + (v) = {u,v}∈E(G) f ({u, v}) is a one-to-one map. The integer-antimagic spectrum of a graph G is the set IAM(G) = {k : G is Z k -antimagic and k ≥ 2}. In this paper, we determine the integer-antimagic spectra for all Hamiltonian graphs.