The performance of old stone and adobe buildings in the 1985 Mexico City earthquake has been in general terms rather satisfactory. Damages were mainly related to previous deterioration due to differential settlements or to weathering and to modifications of the original construction that had weakened the structure. After a general description of the structural problems in the monumental buildings located in the very soft soil of the central area of Mexico City, the paper describes a research program conducted to ascertain the structural seismic safety of a particular type of historic buildings, those used essentially for housing. The research included the identification of the most common structural schemes, the characterization of the materials by in situ and laboratory tests and the determination of the dynamic properties of typical buildings by measuring their vibration under ambient conditions. The main problems that can affect the seismic safety of these structures were identified; particularly critical is the stability under seismic forces of walls that are leaning due to differential settlements of the building. Some design criteria are proposed to take into account these effects. A broader research program is now under way aiming at calibration methods for the linear and non-linear analysis of more complex monumental buildings and at obtaining more information about the mechanical properties of the materials. The main features of this program are outlined.