Introduction Two 4-story reinforced concrete buildings in Fig.2 suffered moderate damage to structures as well as severe damage to nonstructural elements during the 1985 Mexico Earthquake. One month after the earthquake, the buildings were inspected by the authors' team on the level of damage, properties of materials and vibrational characteristics of the buildings and the ground. The inspection was made as a part of activities of the technical mission to the Department of Federal District of Mexico sent by the Japanese Government through the Japan International Cooperation Agency (JICA). After the inspection, further studies were made on their seismic capacity and response so that their behavior during the earthquake and the proposed strengthening methods might be discussed in detail. The Buildings and Their Damage These buildings were constructed in 1982 and have been used as a school for medical students. They were structurally identical except six month different in the completion of construction and different concrete strength by core sampling test. The building W had higher strength (36MPa) than that of another (25MPa). They located at the Transition Zone (Fig.1) and the subsoil consisted of soft clay of 16m thick and of deeper layer of solid sand and other soils (Fig.3). A building consisted of moment-resisting frames of columns and flat slab system called "Losa Plana" (Fig.5). No structural wall was provided. Grouped longitudinal reinforcements were arranged at each corner of a column (Fig.4). The structural damage was concentrated on columns and beams which existed only in the sticking portion be approximately 1 cm or 0.33% to the story height which could lead to moderate or partially severe damage to structures, though it is much less than the yield displacement. The displacement at upper stories is minor. These results well agree with the feature of observed damage. 2) The response dispacement is higher by approximately 50% when subjected to the recorded motion of SCT. 3) The strengthening by concrete walls leads to very minor displacement even during the motions of 1.5 to 2.0 times the intensity of simulated motion. 4) When most columns are reinforced, the structure is able to resist even an earthquake of 2 times the intensity of the simulated motion without any brittle failure. Conclusions 1) It is presumed that the ground motion at the building site would have possessed the characteristics of shorter period and lower intensity compared with those in the Lake Zone. 2) The damage to structures, bond-splitting failure in one building and flexural failure in another, would have occurred because of the lack of lateral stiffness and capacity, the grouped reinforcement with thin concrete cover and the difference of concrete strength. 3) It is presumed that the maximum story drift during the earthquake would have been around 0.3%, which was much less than the yield displacement. 4) Their seismic performance will be significantly improved when they are strengthened by concrete walls or reinforcement of columns.