The periodic eta-invariant is the non-local term in the index theorem for end-periodic Dirac operators due to Mrowka, Ruberman, and Saveliev. It plays a role in a Witten-style conjecture relating the Donaldson and Seiberg-Witten invariants for manifolds with integral homology of S^1 x S^3. It is also used to study metrics of positive scalar curvature. In this talk I will show that, on a manifold with sufficiently long neck, the periodic eta-invariant equals the classical eta-invariant of Atiyah, Patodi, and Singer. This is a joint work with Jianfeng Lin and Daniel Ruberman.