This paper studies the impact of nonlinear distortions on linear system identification. It collects a number of previously published methods in a fully integrated approach to measure and model these systems from experimental data. First a theoretical framework is proposed that extends the linear system description to include the impact of nonlinear distortions: the nonlinear system is replaced by a linear model plus a nonlinear noise source. The class of nonlinear systems covered by this approach is described and the properties of the extended linear representation are studied. These results are used to design the experiments; to detect the level of the nonlinear distortions; to measure efficiently the 'best' linear approximation; to reveal the even or odd nature of the nonlinearity; to identify a parametric linear model; and to improve the model selection procedures in the presence of nonlinear distortions. (C) 2004 Elsevier Ltd. All rights reserved.