AbstractIn earthquake engineering, seismic ground motions are most often modelled as a nonstationary Gaussian process. A few studies indicated that seismic ground motions should be treated as a nonstationary non-Gaussian process, by showing that the kurtosis coefficient of the historical ground motion records is much greater than three. These findings and conclusions are queried in the present study, which analyzes a large number of historical ground motion records. Our results indicate that while the mixture marginal distribution of the acceleration of the records is non-Gaussian with a heavy distribution tail, the mixture marginal distribution of the standardized record, defined by the time-varying record to its standard deviation, is only mildly non-Gaussian. We point out that the mixture marginal distribution of a nonstationary Gaussian process may not be Gaussian. The implication of these observations in simulating records is explained. The sampled nonstationary Gaussian/non-Gaussian records are used to compare the responses of single-degree-of-freedom systems. The results indicate that the error introduced by adopting the Gaussian assumption is small, suggesting that the ground motions could be assumed to be a nonstationary Gaussian process with sufficient accuracy, especially if structures that are not very stiff are considered.