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SummaryThe eigen characteristics of a dynamical system offer a vector sub-space suitable for performing canonical transformations on the system of equations of the structural dynamics problems being considered. While the concept is mathematically fully developed for both damped and undamped systems, practitioners --at all levels --tend to indiscriminately use the system's normal modes as a basis for applications containing nonproportional damping. Such a practice in most cases is a reasonable approximation and results in small, if not infinitesimal, errors. However, with the increase of sophistication and accuracy requirements in certain applications of modal analysis, these approximations must be fully analyzed and understood.In this paper, emphasis is directed to some specific applications for which it is generally a common practice to use normal, or undamped, modes as a vector subspace for use with nonproportionally damped system. These are: Detailed background on complex modes is presented. Commonly used transformations are examined and error models are derived and quantified.