S U M M A R YThe stable estimation of multifractal characteristics of seismicity is considered. The data are world and accessible regional catalogues of m ≥ 2-4 events. Our attention is focused on the range of scales in which the Renyi functionals admit of scale-invariant behaviour. We find that the stable fractal analysis of hypocentres is generally difficult. As to epicentres, we have carried out a stable analysis for seven regions worldwide in the range of scales 1-1.7 decades. The estimates of generalized dimensions admit of tectonic interpretation.