Spin-polarized echo-detected electron paramagnetic resonance (EPR) spectra and the transversal relaxation rate T2(-1) of the photoexcited triplet state of fullerene C60 molecules were studied in o-terphenyl, 1-methylnaphthalene, and decalin glassy matrices. The model is composed of a fast (correlation time approximately 10(-12) s) pseudorotation of (3)C60 in a local anisotropic potential created by interaction of the fullerene molecule with the surrounding matrix molecules. In simulations, this potential is assumed to be axially symmetric around some axis of a preferable orientation in a matrix cage. The fitted value of the potential was found to depend on the type of glass and to decrease monotonically with a temperature increase. A sharp increase of the T2(-1) temperature dependence was found near 240 K in glassy o-terphenyl and near 100 K in glassy 1-methylnaphthalene and decalin. This increase probably is related to the influence on the pseudorotation of the onset of large-amplitude vibrational molecular motions (dynamical transition in glass) that are known for glasses from neutron scattering and molecular dynamics studies. The obtained results suggest that molecular and spin dynamics of the triplet fullerene are extremely sensitive to molecular motions in glassy materials.