This paper studies the asymptotic behavior of nonparametric and parametric frequency domain identification methods to model linear dynamic systems in the presence of nonlinear distortions under some general conditions for random multisine excitations, In the first part, a related linear dynamic system (RLDS) approximation to the nonlinear system (NLS) is defined, and it is shown that the differences between the NLS and the RLDS can be modeled as stochastic variables with known properties, In the second part a parametric model for the RLDS is identified, Convergence in probability of this model to the RLDS is proven, A function of dependency is defined to detect and separate the presence of unmodeled dynamics and nonlinear distortions and to hound the bias error on the transfer function estimate.