Multiple acceleration sequences of earthquake ground motions have been observed in many regions of the world. Such ground motions can cause large damage to the structures due to accumulation of inelastic deformation from the repeated sequences. The dynamic analysis of inelastic structures under repeated acceleration sequences generated from simulated and recorded accelerograms without sequences has been recently studied. However, the characteristics of recorded earthquake ground motions of multiple sequences have not been studied yet. This paper investigates the gross characteristics of earthquake records of multiple sequences from an engineering perspective. The definition of the effective number of acceleration sequences of the ground shaking is introduced. The implication of the acceleration sequences on the structural response and damage of inelastic structures is also studied. A set of sixty accelerograms is used to demonstrate the general properties of repeated acceleration sequences and to investigate the associated structural inelastic response.