Continuous-wave X-band electron paramagnetic resonance (EPR) of fullerene C(70) molecules excited to a triplet state by continuous light illumination was studied in molecular glasses of o-terphenyl and cis/trans-decaline and in the glassy polymers polymethylmethacrylate (PMMA) and polystyrene (PS). Above ∼100 K, a distinct narrowing of EPR lineshape of the triplet was observed, which was very similar for all systems studied. EPR lineshape was simulated reasonably well within a framework of a simple model of random jumps, which implies that the C(70) molecule performs isotropic orientational motion by sudden jumps of arbitrary angles. In simulations, a single correlation time τ(c) was used, varying in the range of 10(-7)-10(-8) s. Near and below 100 K electron spin echo (ESE) signals were also obtained which were found to decay exponentially. Correlation times τ(c) obtained from simulation of the EPR spectra in the slow-motion limit (τ(c) close to 10(-7) s) turned out to be in good agreement with the phase memory times T(M) of the ESE decay, which additionally supports the employed simple model. The observed motional effects provide evidence that the nanostructure of the solid glassy media of different origins is soft enough to allow a large asymmetric C(70) molecule to reorient rapidly. Except for the EPR spectra of the triplet, in the center of the spectra, a small admixture of a narrow line was also observed; its possible nature is briefly discussed.