Near-field (NF) earthquakes have drawn considerable attention from earthquake and structural engineers. In the field of earthquake engineering, numerous studies have identified the devastating nature of such earthquakes, and examined the characteristics related to the response of engineering structures to these types of earthquakes. Herein, special steel moment frames (SMFs) of three-, five-, and eight-story buildings have been examined via a nonlinear time history analysis in OpenSees software. The behavioral seismic differences of these frames have been evaluated in two states: (1) under the simultaneous excitation of the horizontal and vertical constituents of near-field earthquakes that have Fling-steps in their records; and (2) under simultaneous excitation of the horizontal and vertical constituents of far-field (FF) earthquakes. In addition, during modeling, the effects of panel zones have been considered. Considering that the simultaneous effects of the horizontal and vertical constituents of near-field earthquakes were subjected to a fling-step resulting in an increased inter-story drift ratio, the horizontal displacement of stories, an axial force of columns, created the moment in columns, base shearing of the structure, and velocity and acceleration of the stories.