Abstract: The seismic fragility in 2nd-generation performance-based earthquake engineering (PBEE) generally refers to the seismic capacities of both structural components and non-structural components. However, this concept is different from the definition and the content of seismic fragility in traditional seismic risk theory. To clarify the differences between the two fragility definitions, the definition and its probabilistic model for seismic fragility in traditional seismic risk theory are firstly introduced. And then, five seismic fragility models in 2nd-generation PBEE are identified:seismic demand fragility model, seismic capacity fragility model, seismic damage fragility model, seismic loss fragility model, and seismic decision fragility model. The differences and their relationships of the five seismic fragility models are pointed out. The analytical formulations for the probability models and their distribution parameters in a seismic demand fragility model and a seismic damage fragility model are derived. On the basis of the above theoretical deduce, the concepts of forward PBEE and backward PBEE are put forward according to the directions of uncertainty propagation. Through this new concept, the risk integration equation in 2nd-generation PBEE can be solved by different methods. By integrating the approximate formulation of seismic hazard and the analytical formulations of fragility probability models and their distribution parameters, the three probabilistic seismic risk formulations with the same formats for EDP, DM and DV levels are obtained via the methods of forward PBEE and backward PBEE. Through the study of this paper, the traditional seismic risk theory and the 2nd-generation PBEE are unified into a consistent theoretical framework.