The analysis of the statistical structure of the ranges is carried out, the degree of synchronism of fluctuations in runoff characteristics is estimated, and linear trends are identified. The annual values of groundwater runoff have been determined as the arithmetic average of the monthly average minimum winter and summer-autumn water discharges, the surface runoff being calculated as the difference between the annual and groundwater runoff. The stationarity of most of the considered ranges proves to be violated by dispersion or average value. For underground runoff, the number of such ranges according to the Fisher and student criteria is 9 and 12, and for surface runoff, 7 and 9, respectively. For 15 rows of underground runoff and 9 rows of surface runoff, autocorrelation coefficients are statistically significant at a 5 % level of significance. Differential integral curves have been drawn according to the data of each river, the temporal indicators of various phases of water content being determined from them. For the long-term, fluctuations of the underground flow of all the studied rivers are characterized by the presence of a prolonged low-water phase. To quantify the degree of synchronism of long-term fluctuations in the underground flow of rivers, the pair correlation coefficients between all the analyzed series have been calculated. In the long-term fluctuations of both the underground and surface runoff of the rivers of the Greater Caucasus, asynchrony has not been detected. Over the long-term observation period, the underground runoff of the vast majority of rivers is shown to be increasing. For ranges of surface runoff, multidirectional trends have been found. Most of the linear trends in groundwater flow and half of the trends in surface runoff are statistically significant. The significance of linear trends has been estimated by the values of the pair correlation coefficient and its standard error. The data on the runoff of 17 hydrological observation points covering 1934—2017 period have been used