It is recognized that the spatial variability of the ground motion has an important effect on the seismic responses of extended structures, but it is not well known how these structural responses will be affected. The aim of this study was to gain insight of the effect of asynchronous inputs on the elastic and inelastic responses of long bridges in order to improve the earthquake resistant design of bridges. In this research, a simple method of generating the asynchronous input motions, conditioned by the recorded time-histories, is proposed. Two assumptions were adopted in this method. The first assumption was that the spatial correlation function depended only on the predominant frequency of the earthquake motion. The second assumption was that in the time domain, there was no correlation between the acceleration elements in the same record. With the aid of these two assumptions, the modified Kriging method proposed by Hoshiya could be easily used to simulate ground motions in the time domain. Numerical examples showed that the spectra of simulated time-histories and the specified earthquake record closely correlated with each other and the variation of the simulated accelerations with the separation distance between the supports, the propagation velocity and the dispersion factor followed the trends expected. It was observed that the velocity of propagation of seismic waves had a significant effect on the transverse response of long bridges in travelling wave cases. The transverse responses of the bridges to the travelling waves can be more critical than those to the synchronous input. The transverse response parameters investigated were the maximum pier drifts, the maximum pier shear forces and the maximum section curvature ratios of the piers. The responses of the bridges subjected to asynchronous inputs consist of two parts: the dynamic components induced by the inertial forces and the pseudo-static components due to the differential displacements between the adjacent supports. The response was dominated by the pseudostatic component when the travelling wave velocity was low. The pseudo-static component reduced and the dynamic component increased as the travelling wave velocity increased. The response was dominated by the dynamic component when the travelling wave velocity was high. The local variations of the responses with the travelling wave velocity were due to the variations in the acceleration spectra of the input motions with the travelling wave velocity. It was found that the geometric incoherence effect also played an important role in the responses of the bridges through the pseudo-static components. In the cases that the combined geometric incoherence and wave passage effects of the spatial variability of the seismic motion were considered, the pseudo-static component of the seismic response of long bridges was not only caused by the wave passage effect, but was also due to the geometric incoherence effect. The pseudo-static component caused by the geometric incoherence effect dominated the total responses when wave dispersion was greatest. Because the variations of the accelerograms at different pier supports were random, the value of the pseudo-static component due to the geometric incoherence effect was also random. Therefore the total responses were unpredictable when the wave dispersion was great. The influence of the pseudo-static component in the total response decreased as the wave dispersion decreased. When dispersion was least the trends of the variations of the response with the travelling wave velocity were similar to those for the travelling wave cases without wave dispersion. The longitudinal responses of the bridge models with movement joints subjected to asynchronous inputs were also investigated. It was found that the relative displacement of the bridge deck across the movement joints and the relative displacement between the girder end and the top of the abutment consist of two parts: the dynamic components due to the difference between the vibrations of the two frames separated by the movement joints and the pseudo-static components caused by the phase shifts between the vibrations. The dynamic components changed with the travelling wave velocity due to the changes of the acceleration spectra in the asynchronous motion cases. The pseudo-static components were not only dependent on the phase shifts, but were also related to the shapes of the response displacement time-histories of the bridge deck.