Nanoparticles (mean size about 7 nm) of the standard pyrogenic Aerosil 1380 (Degussa) pregrafted by γ-irradiation with styrene were melt-compounded with the general purpose isotactic polypropylene homopolymer to prepare four nanocomposites with filler volume contents up to 4.68%. Storage G′( ω) and loss G″( ω) shear moduli in the melt state (measured in the range of linear viscoelasticity at three temperatures in the frequency window spanning about three decades) were treated to derive the relaxation times spectra h( τ) using the NLREG computer program based on Tikhonov’s method of non-linear regularization. The experimental data were interpreted in terms of the tentative model highlighting the structural significance of the ratio of mean thickness of polymer interlayer between neighboring filler particles, 〈 L〉, to the mean radius of gyration of a polymer coil, 〈 R g〉. In the range of very low filler loadings characterized by large scaled distances, 〈 L〉/〈 R g〉≥1, all nanocomposites behaved as Newtonian liquids in which the self-diffusion of macromolecular coils was, however, slowed down. The onset of plastic yield phenomenon for a nanocomposite with the filler volume content as low as 4.68% was regarded as the experimental evidence for the shear-resistant, infinite cluster of filler particles coated with polymer boundary interphase when the scaled distance approached the “critical” value, 〈 L〉/〈 R g〉≤1.