The seismic soil response can be analyzed in the frequency as well as in the time domain). The nonlinear constitutive properties of soils being difficult and costly to determine, the present work proposes a simplified constitutive model to analyze the dynamic soil response for moderate or strong earthquakes at large scales (alluvial basins). In this work, we consider a non linear viscoelastic constitutive model involving both non linear elasticity as well as non linear viscous behavior. The non linear elastic part of the model is described by a hyperbolic law. The description of the viscosity starts from a Nearly Constant Quality Factor (NCQ) model able to fulfil the causality principle for seismic wave propagating in dissipative materials. In the NCQ model, we introduced a dependence on the excitation level in order to consider the variations of moduli and the increasing damping ratio. Starting from the proposed mechanical formulation, the analysis of the nonlinear response of a sedimentary layer submitted by a vertical SH wave is then performed (finite element method). For large excitation levels, the analysis of wave propagation in sedimentary layer leads to interesting results: at the free-surface the spectral peaks are shifted to lower frequency values; higher frequency components are not overdamped as for the equivalent linear model; the amplification level is generally lower. These results show the ability of this simplified nonlinear model to investigate, in the near future, site effects in 2D/3D alluvial deposits for strong earthquakes.