Besides seismic base isolation [1,2] and other strengthening techniques [3], the use of fluid viscous dampers (FVDs) as energy dissipation devices has rapidly increased in the last few years [4] for seismic retrofitting of existing civil engineering structures. Their appealing properties include the large energy dissipation capability, the low maintenance required, and the generation of forces that are out of phase with the elastic forces, thereby not increasing the stress in the structure. Experimental evidence [5–۹] reveals that the constitutive behavior of FVDs can be described by a fractional velocity power law f = cu u | | sgn( ̇ ̇) NL α d d (1) where cd is the damping coefficient, α is a velocity exponent, u̇ represents the relative velocity at the ends of the device and sgn(⋅) is the signum function. The exponent α is responsible for the nonlinear damping of FVDs and depends upon the hydraulic circuit employed. Typically, α ranges from 0.10 to 0.50 for seismic applications. As a result of the nonlinear constitutive behavior of FVDs, linear methods of analysis, e.g., the response spectrum method, are no longer applicable. In this regard, attempts have been made to determine an equivalent viscous damping ratio due to the added nonlinear FVDs [10], or an equivalent damping coefficient of energy-equivalent FVDs associated with the same energy dissipation as the nonlinear FVDs [11]. The above-mentioned relationships, extremely useful for preliminary design purposes, are amplitude-dependent due to the nonlinear nature of FVDs. Furthermore, they are strictly valid under the hypothesis of harmonic motion. Since the earthquake-induced motion is not really harmonic but is generally modelled as a random process, the estimation of the equivalent damping coefficient can be alternatively performed within the framework of the stochastic linearization technique (SLT) [12]. The SLT was applied in a number of research papers and to a general class of nonlinear behaviors, not just confined to the one shown in (1), e.g.: in the context of tuned liquid column damper optimization [13,14], characterized by quadratic-times-signum-like damping; in the field of nonlinear energy sinks optimization [15], featured by a cubic stiffness; for optimizing the performance of hysteretic dampers [16], represented by a Bouc-Wen model. The SLT has also been successfully applied to derive equivalent linear properties of bilinear systems [17,18] in the framework of response spectrum analysis [19,20]. Coming back to the nonlinearity of FVDs given by (1), which is of interest to the present note, in the literature the SLT has been applied by introducing the stochastic nature of the earthquake input via a powerspectral-density (PSD) function S ω ü ( ) g , for example the Kanai-Tajimi PSD [21–۲۳], or a particular spectrum-compatible PSD function [24,25]. All these quoted papers used a popular force-based Gaussian SLT (F-G-SLT). In this note, it is demonstrated that this variant of SLT is not the best option for the kind of nonlinearity induced by the FVDs. After a critical assessment of six alternative formulations of SLT, we identify a so-called equal-energy non-Gaussian SLT (EE-NG-SLT) that, without increased computational effort, is better able to capture the nonlinear response of the system.