Electron-spin-echo experiments at 9 and 95 GHz on the triplet state of C-70 in glassy matrices are reported. Analysis of the echo decays as a function of the time after laser excitation allows a complete description of the distinct population and decay of the substates-of the lowest triplet state of this fullerene at 1.2 K. The observation of spin-lattice relaxation between the triplet sublevels reveals pseudorotation of the C-70 molecule about its long axis on a time scale of microseconds even at such a low temperature. The fine-structure parameter D of triplet C-70 is found to be positive.