Title: Harmonic-Killing vector fields Authors: C.T.J. Dodson, M. Trinidad P\'erez and M.E. V\'azquez-Abal Abstract: In this paper we consider the harmonicity of the 1-parameter group of local infinitesimal transformations associated to a vector field on a (pseudo) Riemannian manifold to characterize intrinsically a new class of vector fields, which we call harmonic-Killing vector fields. 2000 Mathematics Subject Classification: 53C43, 53C55, 53B20.