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This article presents a methodology to assess the seismic vulnerability of essential buildings through analytical fragility curves, applied to the administrative building of the Universidad Nacional del Centro del Perú, for various damage states and different levels of seismic demand according to ATC-40 and SEAOC -VISION 2000. It is shown that the fragility curves through the probability of damage matrices allow us to reasonably estimate the probable state of the building after a seismic event, which in the case of the building under analysis shows that it is more vulnerable in the North-South direction (Y axis). [ABSTRACT FROM AUTHOR]