In civil and mechanical engineering, it can be very difficult and expensive to excite existing real-scale constructions for identification purposes. The classical identification procedures in frequency domain such as Peak-Picking, Frequency Domain Decomposition, Maximum Likelihood Identification, return good results under the assumptions that the excitation is white noise, the structure is lightly damped and the modes are well sepa-rated. For instance, when the white noise assumption is violated, the components of exci-tation frequency spectra cannot be separated from the eigenfrequencies of the system. A new identification procedure to extract both structural and excitation parameters for white and coloured input using output-only responses is presented, assuming a paramet-ric model of the power spectral density (PSD) matrix of the response. A minimization cri-terion for the difference between the norm of the PSD matrices of the model and that of the measured response is proposed. An optimisation problem is solved which allows to separate possible frequency components of the unknown excitation from the system ei-genfrequencies. The proposed technique is validated on a linear 3-DOF shear-type frame under base excitation and on a 2-DOF piecewise-linear oscillator.