In this paper a cable-stayed bridge and a suspension bridge with closer main span lengths are considered to determine the effects of near-fault and far-fault ground motions on the structural responses of these bridges under asynchronous excitations. While the Tatara Cable-Stayed Bridge constructed in Japan is preferred as a cable-stayed bridge model, the Fatih Sultan Mehmet Bridge constructed in Turkey is considered as a suspension bridge model. While the geometric nonlinearity including P-delta effects resulting from the self weight of the suspension bridge is considered in the dynamic analysis of the suspension bridge, the nonlinearity of the cable-stayed bridge cables are taken into account with the equivalent modulus of elasticity. The results show that the traveling wave has a complicated effect on the structural responses like displacements and internal forces, and underestimates or overestimates the structural responses depending on the wave propagation velocity and the considered structural responses. It is also observed that the increment of the responses for the infinitely propagating near fault ground motions with respect to the farfault ground motions are obviously larger than the incerement obtained for the 250 m/s wave propagation velocity.