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The complex torque coefficients method has been widely accepted for the analysis of the phenomenon of torsional interaction of turbine-generator units in power systems. This paper shows that, depending on the system parameters and the operating point, the complex torque coefficients method may exhibit limitations and not accurately and fully predict the system behavior in the frequency range of interest. These shortcomings consist of inability to i) predict monotonic instability due to real poles, ii) identify all electromechanical oscillatory modes, and iii)accurately predict damping (and consequently stability) of the oscillatory modes. This paper develops mathematical expressions to highlight the limitations of the complex torque coefficients method. Quantitative results based on three case studies, including a study on the first IEEE Benchmark System, are reported and results from eigenvalue analysis method, complex torque coefficients method, and time-domain simulation are presented and compared. This paper concludes that the complex torque coefficients method can be used only as a preliminary method for the investigation of torsional interactions and the results must be verified by other methods.