Two complete sets of records obtained from a strong-motion accclerograph array in the Gisborne Post Office building during earthquakes of 1982 and 1993 were analyzed by using systems identification techniques to estimate the modal parameters. Nonlinear responses of the soil-structure system in both horizontal and vertical directions were indicated by significant decreases in the estimated first mode frequencies for moderate to strong ground motion in 1993 compared to those for the small amplitude ground motion in 1982. The analysis of second floor and remote site records from a 1985 earthquake indicated that nonlinear responses also occurred then. Soil-structure interaction was found to be significant for both vertical and horizontal responses. Using a numerical model of the foundation-soil system, the foundation rocking frequency and first fixed-base modal frequency were estimated. It was found that frequencies of the building's first fixed-base mode, foundation translation and rocking all were reduced in the 1993 earthquake compared with those of the 1982 earthquake, indicating that nonlinear responses occurred in both the building and the soil in the 1993 earthquake. Possible evidence for a cutoff frequency at the soil site was also identified. Because of soil-structure interaction, the fixed-base horizontal response in the N44E direction was reduced by possibly 40-50% in the 1982 earthquake, and about 30% in the 1993 event, compared with the recorded first modal response of the soil-structure system.