In this paper, lateral torsional response characteristics of single-story one-way and two-way torsionally coupled systems and also multi-story torsionally coupled systems when subjected to ground motions are investigated based on a random vibration approach. The principal conclusions are summarized as follows : 1) The two variables, those are eccentricity e_y/γ and frequency ratio ζ_<xθ>, are most closely related to torsional response of structures subjected to ground motions. 2) A dynamic torsional amplification factor A_d, which is defined by A_d=dynamic torsional displacement/static torsional displacement, gives a predominant peak at ζ_<xθ>&nap;1 on an A_d-ζ_<xθ> plane. In this case, the smaller the value of e_y/γ, the sharper the peak. The maximum value of the factor A_d is experimentally given by Eq. 43. 3) The eccentricity factor R_<ex> defined in the Building Standard Law is approximatey equal to an eccentricity constant θ_x which is defined as a product of two variables e_y/γ and ζ_<xθ>, if the value of R_<ex> is not greater than 0.6. 4) Response of a two-way torsionally coupled system which has the frequency ratio ζ_<xθ> less than 1 〜 1.5 can be estimated from the one of a one-way torsionally coupled system. 5) Torsional displacement ru_θ/u_x at the story with eccentricity of a multi-story system approximately coincides with the one for a corresponding single-story system if ζ_<xθ>≦1, and generally gives smaller values compared with the single-story one in case of ζ_<xθ>>1. 6) Torsional displacement at the story without eccentricity of a multi-story system is negligibly small in case of ζ_<xθ>≦O.5. However, it rapidly becomes larger with larger value of ζ_<xθ>, and, is expected in some case to be larger than the one which is produced at the story with eccentricity.