Linear system identification [1]-[4] is a basic step in modern control design approaches. Starting from experimental data, a linear dynamic time-invariant model is identified to describe the relationship between the reference signal and the output of the system. At the same time, the power spectrum of the unmodeled disturbances is identified to generate uncertainty bounds on the estimated model. Linear system identification is also used in other disciplines, for example vibrational analysis of mechanical systems, where it is called modal analysis [5], [6]. Because linear time-invariant models are a basic model structure, linear system identification is frequently used in electrical [7]-[10], electronic, chemical [11], civil [12], and also in biomedical applications [13]. It provides valuable information to the design engineers in all phases of the design process.Starting from the late 1960s, system identification tools have been developed to obtain parametric models to describe the dynamic behavior of systems. A formal framework is set up to study the theoretical properties of the system identification algorithms [1]- [3]. The consistency (does the estimated model converge to the true system as the amount of data grows?) and the efficiency (is the uncertainty of the estimated model as small as possible?) are analyzed in detail. Underlying all these results are the assumptions that the system to be modeled is linear and time invariant.It is clear that these assumptions are often (mostly?) not met in real-life applications. Most systems are only linear to a first approximation. Depending on the excitation level, the output is disturbed by nonlinear distortions so that the linearity assumption no longer holds. This immediately raises doubts about the validity of the results obtained and validated by the linear system identification framework. The term nonlinear distortions indicates that nonlinear systems with a (dominant) linear term are considered. The deviations from the linear behavior are called nonlinear distortions.