This paper studies the dynamic responses of SDOF system under pulse-dominant excitations. The purpose of the study is to prepare for scrutiny of some near-field pulse-dominant ground motions and their potential to cause structural damage. Extending the single pulse dynamics, we consider the effect of pulse sequences. This kind of excitation was particularly obvious in some of previous earthquakes such as Northridge (1994) and Chi-Chi (1995). Based on the duration,peak and rise and decay era of the main pulse as well as its relationship with the predecessor and successor pulses, we propose a classification for the pulse sequences. Consequent studies have been carried out for acceleration, velocity and displacement response spectra of the main pulse with either a predecessor or a successor pulse. The analysis also includes general response behaviors in different fundamental period segments and special aspects of response at certain points (e.g., the corresponding peak points).