Strong ground motion close to a fault can be expected to be very large, so its estimation is essential for human safety. Although a few strong-motion data exist for the west Eurasian region, we proposed in a previous work an attenuation relation for spectral acceleration using strong-motion data recorded in west Eurasia (mainly in Europe) and some in the western united states: this relationship was derived for the French Safety Rule, which is applied for seismic hazard assessment at nuclear power plants. In this study, we propose a constraining of the amplitude saturation term related to the proximity of the fault, and an adding of an amplitude saturation term in the regression model. We add to the data-set previously used to derive the west Eurasian attenuation relationship strong-motions recorded during recent large earthquakes: the 1995 Hyogo-ken Nanbu (Kobe) event in Japan and the 1999 Kocaeli (Izmit) event in Turkey. The regression analysis, adopted from Fukushima and Tanaka (1990), is non-linear, so an iterative procedure is applied. The determined regression coefficients lead to a prediction of a peak ground acceleration of about 0,7g for soil site conditions at a fault distance of 0,5km. The Q coefficient deduced from the distance coefficient is in agreement with scattering Q models. The introduction of the saturation term leads to significantly lower predictions of average spectral accelerations at short distances as compared with using the Berge-Thierry et al. (2003) empirical model.