The present paper investigates a time-domain harmonic balance method as an alternative to classical time-marching schemes for the stability study of turbomachineries toward flutter. This study is performed in a weak coupling approach, which requires to compute the fluid response to prescribed harmonic motions of the structure. The harmonic balance method is adapted to single sector reduction and an arbitrary Lagrangian/Eulerian formulation. Two different industrial test cases are presented: an axial compressor used in a Turbomeca helicopter engine and a fan designed by Snecma. The results show the good accuracy of the proposed harmonic balance method as well as significant reductions in computational costs.