This paper presents the basic concepts and the analytical formulation of the “FNA” (Fast Nonlinear Analysis) method for the solution of dynamic computational problems with a small number of nonlinear elements, as in the case of building structures incorporating special seismic protection technologies. The method is then applied to an experimental single-story steel frame and a multi-story reinforced concrete frame building, both equipped with dissipative braces incorporating “ADAS” or fluid-viscous devices. The results of these applications are finally compared to the ones of the same analyses carried out by a step-by-step integration method.