We show that strong response to non-resonant modulations and excess noise are state dependent in generic nonlinear systems, i.e. they affect some output states, but are absent from others. This is demonstrated in complex Swift-Hohenberg models relevant to optics, where it is caused by the non-normality of the linearized stability operators around selected output states, even though the cavity modes are orthogonal. In particular, we find the effective parameters that control excess noise and the response to modulations and show cases where these phenomena are enhanced by an order of magnitude.PACS numbers: 42.65. Sf,42.60.Mi,42.55.Ah Excess noise [1] is a term used in optical device physics to highlight the fact that the sum of the energy in the individual modes is greater than the total energy available. This phenomenon was first predicted by Petermann in [2] and its paradoxical result was explained in [3]: the modes of excess noise systems are correlated (non-orthogonal). Therefore, the total energy cannot be written as the sum of the energies of the individual modes since one must include the mode-mode correlation terms too. Usually, the "modes" referred to in the explanation of this phenomenon have been interpreted as modes of the optical cavity, either open [4] or unstable [5] or with misaligned elements [6]. However, the "modes" in question are far more general: they are the modes of the dynamics of the system [7]. In this respect excess noise is just one aspect of the enhanced response to modulation and transient growth typical of non-normal operators, i.e. operators that do not commute with their adjoint [8,9]. The main feature of non-normal operators is that their eigenvectors are not orthogonal. This can have dramatic consequences in terms of the dynamics of the system: perturbations of stable states can be substantially amplified before they eventually decay (transient growth) [8]; the response to an external modulation can be very large even far from resonance (pseudo-resonance) [10]. An essential point often overlooked is that when the system under investigation is nonlinear, then the operator responsible for these effects is the linear stability operator and this is state, not just model, dependent. This is particularly important when studying systems that are both timeand space-dependent and have a rich bifurcation structure. Enhanced response to external modulations critically affects, for example, the implementation of chaos synchronization in secure laser communications [11].In this letter we analyze three aspects of generic nonlinear systems. First of all primary bifurcation of a given state may be normal, while its secondary bifurcations, in general, are not. Secondly, the effects of non-normality on the nonlinear dynamics and response can vary from state to state and need to be quantified. Thirdly, the system response depends on the spatial and temporal frequency of the modulation. This opens the possibility of fine tuning the output of the system by carefully choosing the modulation wave ...