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This paper deals with the parameters which influence the probability of reaching the near collapse limit state of RC frame structures equipped with nonlinear fluid viscous dampers. The study can be divided into two steps. The first aims to assess how the median and the dispersion of seismic demand can vary in the RC frame structures with and without dampers, considering a wide set of ground motions. The second step evaluates the expression in closed form, given by 2000 SAC/FEMA method, to assess the annual probability of failure of RC structures. This probability has been estimated considering a wide set of ground motions and different methods to approximate the hazard curve. The evaluations have been made on the basis of the results of a large number of nonlinear dynamic analyses; in particular, 180 nonlinear dynamic analyses have been made for the case studies with and without dampers. In conclusion, it has been noticed that the probabilistic assessment depends on the number of records considered and that the simplified formula provided by the 2000 SAC-FEMA method is strongly sensitive to the variation of the hazard curve and the dispersion.