Well-known methods of spectral analyses and system identification are used to analyze a set of 11 acceleration records obtained between November 1992 to December 1999 from a 14-storey reinforced concrete building founded on soft soil in Mexico City. The building has been repaired twice during its lifetime. The first retrofit was in 1986 due to the structural damage produced by effects of the M, = 8.1, 1985 Michoacán earthquake in Mexico City. Because of the deficient behaviour of the structure observed as a consequence of moderate intensity earthquakes between 1986 and 1995, it was then upgraded again. The purpose of this paper is to study the main features of the seismic response of the building and its interaction with the soil when subjected to several small and moderate size earthquakes in a seven-year period. From the analysis of the seismic records, variations of natural frequencies and damping of the soil-structure system were observed. It was found that the dynamic properties of the system are very sensitive to the intensity of the ground shaking. Significant stiffness degradation of the building was found as well. The variation of structural parameters of the system can be attributed mainly to different nonlinearity sources of the structure.