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In many engineering applications, linear models are preferred, even if it is known that the system is nonlinear. A large class of nonlinear systems can be represented as Y = G BLA U + YS, with G BLA being the best linear approximation and YS being a nonlinear noise source that represents that part of the output that is not captured by the linear approximation. Because G BLA not only depends upon the linear dynamics but also on the nonlinear distortions, it will vary if the input power is changed. In this paper, we study under what conditions (class of excitations and class of nonlinear systems) these variations of G BLA can be bounded, starting from the knowledge of the power spectrum SYS. In general, without a restriction of the class of systems, no upper bound can be given. However, for some important classes of systems, the variations can be bounded by selecting a well-defined criterion. Since SYS can easily be measured using well-designed measurement procedures, it becomes possible to provide the designer with an upper bound for the variations of G BLA, leading to more robust design procedures.