The paper examines the effects of nonlinear distortions on the frequency domain estimation of linear models using multisine test signals. It is shown that odd-order nonlinearities will always introduce an error, the magnitude of which depends on the interaction of different types of nonlinear components, which in turn depends on the type of multisine used. A class of wideband pilot test signals is proposed, termed sparse odd multisines, to establish the system bandwidth and detect nonlinearities. The elimination of the nonlinear effect is then addressed using a two-level multisine test. Finally, a case study is presented which illustrates the application of these techniques to gas turbine modelling.