A highly efficient seismic protection of bridges have been demonstrated by the passive control systems with mechanical links with selective viscoelastic energy dissipation through viscous friction and dry friction. These systems are able to take over the deformations and movements caused by temperature variations, those due to seismic activities and from road traffic. A number of natural factors such as atmospheric and anthropogenic parameters, such as shock and vibration from road traffic, lead to the degradation of the viscoelastic bonds of passive control systems based on rubber molding. The presence of the elastic and dissipative nonlinear forces in the functioning of antiseismic systems inevitably leads to quantitative and qualitative changes of the structural responses of bridges and viaducts both in time and spectral domains. The implications of these changes on the integrity and stability of the bridge or viaduct sections may be from the simplest to the most severe depending on the type of seismic excitation to which they are subjected. For these reasons, it is imperative that we should identify and quantify the degree of nonlinearity of antiseismic systems embedded in the structure of bridges and viaducts in order to prevent accidents with severe socioeconomic implications. In this way can determine the dependence of the nonlinear behavior of the bearing system and the degree of degradation of their viscoelastic links. From a theoretical point of view the following parameters of the vibration of the system will be comparatively analyzed: the displacement and acceleration of the bridge deck in time and frequency domains, the hysteretic loop, the representation in the plane of phases, the power spectral density and the spectrograms of the acceleration signals. From an experimental point of view there will be identified and plotted the parameters able to provide information regarding the abnormal operation of the bearings from the elastomer: system acceleration, representations in time and frequency and its spectrogram.