The model-based identification of frequency response functions is of central importance in the context of the analysis and evaluation of dynamic deformation behavior and process stability of machine tools. The significance of this frequency response is determined essentially by the accurate consideration of damping - in approach and parametric. In the material or the component damping pays an amount very small essential however for the system consideration proportion in the damping effect. This article presents recent results to the efficient experimental determination of the damping and the derivation of appropriate model parameters. It is entered on the specifics of extremely weak damping.