In this work, we consider an extended viscoelastic NCQ model to simulate seismic wave propagation in alluvial basins in the case of strong motions. This constitutive model involves both non linear elasticity and non linear viscous behaviour. The main objective of this model is to reproduce the dependence of the shear modulus and damping on the motion amplitude. To do so, the non linear elastic part of the model is described by a hyperbolic law. The non linear viscous part combines a Nearly Constant-Q model for linear damping and a non linear viscous contribution described by a hyperbolic variation with the strain level. Furthermore, this model complies with the thermodynamic principles of continuum mechanics. Starting from this extended NCQ model, the analysis of strong motion amplification in alluvial deposits is then performed considering a finite element formulation. Detailed validations of the model have shown its ability to recover low amplitude ground motion response. For larger excitation levels, the model includes the main features of the non linear behaviour of alluvial deposits. Realistic simulations are performed for Kushiro-oki earthquake. The analysis of seismic wave propagation in surface layers leads to interesting results: at the free-surface the amplification peaks are shifted to lower frequency values (when compared to the input motion); higher frequency components are not overdamped as with classical linear models and, finally, the global amplification level is generally lower than for weak motions.