Vibrations of the Earth crust and variations in the physical fields of the Earth atmosphere and ionosphere are continuously monitored by a variety of techniques and specialized facilities across the world. Nevertheless, most catastrophic earthquakes even in this century have occurred in "incidental" or "unexpected" places in "unpredicted" time. Earthquake predictions have errors as the current knowledge of focal mechanisms of strong (M≥8) earthquakes is still insufficient. It is believed today that the most common source of earthquakes is movement of rock blocks along a fault/megafracture. Such movements take place in a stepwise pattern with high or reduced friction, depending on the presence of fluids, hitches on the fault planes and other factors. Modern seismic forecasting is based on the concept of precursors.The author considers geological and geophysical settings in areas of dynamic influence of faults, wherein 8>М>7.5 earthquakes took place. Based on earthquake recurrence curves constructed for such areas, four tectonic criteria for formation of strong earthquake sources are identified: structural (large seismically active faults), kinematic (large amplitudes of the fault wing's displacements), rheological (physical properties of the fault infill material, such as low viscosity of the intra-fault medium) and dynamic (high rates of the fault wing's displacements) criteria. These criteria should be in the focus of quantitative studies in order to provide a solid scientific basis for long-term forecasting of strong earthquakes. Curves constructed for the criteria can show changes in the physics of earthquake foci in case of strong seismic events.With account of the tectonophysical features of faults associated with strong seismic events, the following conclusions are drawn. (1) In the continental lithosphere, catastrophic earthquakes (M≥8) occur in areas of dynamic influence of the major faults in the lithosphere in case of relatively high amplitudes of displacements of boundary blocks (i.e. fault wings). (2) In the relatively stable stress field, high amplitude displacements take place in case of reduced viscosity/quasi-viscosity of the medium comprising the internal structure of faults. (3) Reduced viscosity of the intrafault medium is related to the physical conditions of transition of rocks in fault zones (mainly along the fault planes) in the state of quasi-plastic or plastic flow (unilateral pressure in excess of hydrostatic pressure, and relatively decreasing strength properties of the intra-fault medium with increasing length of the fault wings). (4) Reduced viscosity of the fault zone leads to an increase in the displacement rate of the fault wings in the constant stress field. The latter factor is the main one, transforming seismically active faults with M≤7.5 seismic events into faults of similar characteristics, but with earthquakes of higher energy, M≥8. Focal mechanisms of such earthquakes are associated with conditions for a potential increase of the displacement amplitude regardless of the pre...