This paper investigates the seismic behaviour of multi-storey buildings base-isolated by friction pendulum systems. The non-linear equations of motion have been expressed in an original simple form through the use of appropriate Lagrangian parameters. The dynamic response of the system has been evaluated numerically by means of a Fast Nonlinear Analysis based on a co-ordinate Ritz transformation. The adopted Ritz vector basis is represented by the undamped eigenvectors of the structure on a fixed base. Extensive parametric investigations have been performed in order to investigate the non-linear behaviour of multi-storey buildings subjected to harmonic and earthquake excitations. The results, expressed in the frequency domain and in the form of response spectra, allow to compare the dynamic response of the sliding system with the corresponding response of the same structural system on a fixed base.