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Near-fault ground motions with long-period pulses have been identified as critical in the design of structures.To aid in the representation of this special type of motion, eight simple pulses that characterize the effects of either the flingstep or forward-directivity are considered. Relationships between pulse amplitudes and velocity pulse period for different pulses are discussed. Representative ratios and peak acceleration amplification can exhibit distinctive features depending on variations in pulse duration, amplitude and the selected acceleration pulse shape. Additionally, response spectral characteristics for the equivalent pulses are identified and compared in terms of fixed PGA and PGV, respectively. Response spectra are strongly affected by the duration of pulses and the shape of the basic pulses. Finally, dynamic time history response features of a damped SDOF system subjected to pulse excitations are examined. These special aspects of pulse waveforms and their response spectra should be taken into account in the estimation of ground motions for a project site close to a fault.