In the present paper, the Nonlinear Harmonic (NLH) method implemented in Fine/Turbo code has been evaluated for unsteady rotor-rotor interaction analysis. Strengths and weaknesses of the NLH method are highlighted through direct comparison with experimental data and time-domain unsteady simulation for the NWPU counter-rotating research compressor (CRRC) at the design and off-design conditions. The rotor-rotor interactions were studied in detail to advance the understanding of the flow physics involved. Based on the unsteady simulation, deterministic stresses were computed and compared to the NLH method to analyze distinct sources of unsteadiness and their effect on the time-averaged flow field. For the present case, the NLH method is about one order magnitude faster than the direct time-domain method.