Nonlinear dynamic analysis of existing or planned structures often requires the use of accelerograms that match a target design spectrum. Here, our main concern is to generate a set of motions with a good level of fit to the Eurocode 8 (EC8) design spectra for France. Synthetic time series are generated by means of a non-stationary stochastic method. To calibrate the input parameters in the stochastic approach, we select a reference set of accelerograms for a Eurocode 8 type B site category from the PEER Ground-Motion Database, which are then adjusted to the target spectrum through wavelet addition. Then, we compute nonlinear seismic responses of a soil column, including pore pressure effects, and brittle and ductile structures to the stochastic time-series, the natural accelerograms and timeseries generated using stationary stochastic approaches. The results of these calculations reveal considerable variability in response despite the similarities in terms of spectral acceleration.