The problem considered is that of identification of unknown parameters of multivariable, linear "errors-in-variables" models, i,e,, linear systems where measurements of both the input and output of the system are noise-contaminated, Attention is focused on frequency-domain approaches where the integrated polyspectrum (bispectrum or trispectrum) of the input and the integrated cross-polyspectrum, respectively, of the given time-domain input-output data are exploited. Two new classes of parametric frequency-domain approaches are proposed and analyzed. An integrated polyspectrum-based persistence of excitation condition on system input is defined and related to parameter identifiability of the multivariable system. Both classes of the parameter estimators are shown to he strongly consistent in any measurement noise sequences with vanishing bispectra when integrated bispectrum-based approaches are used, The proposed parameter estimators are shown to be strongly consistent in Gaussian measurement noise when integrated trispectrum-based approaches are used, The input to the system need not he a linear process hut must have nonvanishing bispectrum or trispectrum. Finally, two simulation examples are provided to illustrate the two approaches.