Important problems of tectonophysical analysis of observational results in recent geodynamics are considered. The paradox of low rates of recent horizontal deformations of the Earth's surface is formulated. This paradox states that, according to GPS measurements, the annual mean rates of relative deformations are 10(-9)-10(-10) per year, whereas, according to ground-based geodetic and deformographic observations, the rates of recent horizontal deformations of the Earth's surface are on the order of 10(-5)-10(-6) per year. This paradox is shown to appear as a result of the application of the procedure of averaging to the displacements obtained on large measuring bases with a low degree of details of the time of observations. It is established that, according to multiyear (over 40 years) data, the annual mean rate of deformation processes in the Kopet Dagh seismically active region is 4 x 10(-8) per annum along the vertical and 3.2 x 10(-8) per year along the horizontal. The spatial discreteness of anomalous deformation processes along the strike of the regional Rechitsa fault (Pripyat trough) is revealed. It is inferred that the present-day anomalous activity of fault zones must be taken into account, when regional regularities of geodynamic processes are established on the basis of geodetic and geophysical measurements in the real time scale.