The seismic monitoring of buildings is important for two fundamental reasons: - evaluate the possible dynamic behavior of these structures during earthquakes; - gain experience on the general seismic behavior of the structures to permit the use of a database for future design and analysis. The results of previous work in seismic monitoring of the structures permitted the development of a database, which in turn was used in the creation of new formulas and reference values for the estimation of the fundamental periods of the structures and to evaluate the percentage of critical damping from use during dynamic analyzes. The database is very well supplied with data on traditional buildings, but there is still not enough data for buildings with base isolation. Some different structures with seismic base isolation have been monitored during recent strong earthquakes in Italy, namely Amatrice earthquake (2016/08/24, Mw=6.0) and Norcia earthquake (2016/10/30, Mw=6.5). For the structure under examination, in far fault condition, amplification phenomena have been noticed, up to about twice the accelerations on the superstructure, for very low energy value inputs. In these cases, however, it is noticed that the amplified accelerations are extremely small, and very far from being able to damage the structure. Records from the ENEA permanent accelerometric network, installed in the structure under examination, and the tests carried out on the same isolators used for the qualification test of the devices below the analyzed structure, permit to describe the behavior of the isolators in terms of force and displacement defining two non-linear laws, derived from experimental data. The non linear analisys of the building behaviour using the referred experimental laws evidenced the good fitting between experimental data and numerical simulation, while linear analyses evidenced some significant differences.