To solve the complex problems of the genesis and stability of high slopes in mountainous-folded regions, it is important to determine the basic investigation directions, problems, and methods in order to obtain objective, scientifically substantiated results, corresponding to the present-day level of the engineering geology. These problems include: a) ancient and recent tectonical structures, the regime of their movement and seismicity as one of the manifestations of the tectonic processes; b) the rocks, their composition, stratification, texture, initial and tectonical fracturing; c) the geologic history of the genesis of slopes, landslides, earthslips, and earthfalls, and their engineering-geologic classification; d) the development of exogenic processes within the rock masses of the mountainous slope, the formation and expansion of unloading, weathering, and natural stresses zones; e) the evaluation of the ground and atmospheric water as a factor changing the strength characteristics of the crumbling-sliding masses or of the rocks included in the unloading and weathering zones; f) resistance characteristics, deformation properties, and stress conditions of the masses of rock as a whole, and of separate portions which potentially present different stability characteristics; g) assessment of the present stability of the whole slope, and of its various portions, forecast of the landslides and earthslips developing on the slope, including their volume and time of occurrence (the short-term forecast of landslides and earthslips has a large importance); h) recommendation of methods for the consolidation of rocks and slopes to stave off landslides and earthfalls, dangerous both for the permanent structures and for the construction work, measures to be checked for efficiency both experimentally and in natural conditions. Very important is the complexity and coordination of the engineering-geologic studies, including: specialized geologic mapping by means of sophisticated instruments, regime observations, reconnoitering and testing of boreholes and galleries by seismoacoustic methods, experimental and laboratory investigation of the geomechanical and infiltration properties of the rocks and of the stress distribution in the rock masses. The methods of statistical processing of the landslide, earthslip engineering-geologic mapping and fracturing data, as well as the estimation of the slope stability, or of separate masses of rocks contained in it, by computation and modelling methods must find a proper place in the general investigation complex.