This paper presents an evaluation of the multiple-frequency phase-lagged approach, which enables the performance of unsteady Reynolds-averaged Navier-Stokes simulations on multistage turbomachinery configurations using a time-marching method. The major advantage of this approach is to reduce the computational domain to one single blade passage per row. The first part of the paper presents the method and discusses the associated assumptions and limitations. The method is then evaluated on the axial compressor configuration "Compresseur de Recherche pour l'Etude des effets Aérodynamiques et TEchnologiques" investigated experimentally at Laboratory of Fluid Mechanics and Acoustics. The computational fluid dynamics results are analyzed and compared both with experimental data and with a reference multipassage computation based on a sliding mesh approach. These comparisons enable the highlighting of the interests of this approach but also the underlining of its limits. The multiple-frequency phase-lagged approach enables the simulation of unsteady effects on a multistage turbomachinery and access to unsteady information that would not be available with a mixing-plane approach. However, if the method is capable of capturing unsteady effects linked to the adjacent upstream and downstream blade rows passing frequency, it fails modeling clocking effects, i.e., the relative influence between rows N and N 2.