A study of the photoexcited triplet state of C-60 (C-3(60)) in liquid solution (toluene, methylcyclohexane) was made using pulsed-EPR techniques. The spin-lattice relaxation time (T-I), phase-memory time (T-m), and line width (Delta v(1/2)) were measured as function of temperature (170-360 K). The results were used to analyze some aspects of the spin dynamics of C-3(60). The data confirm earlier findings that the relaxation toward Boltzmann equilibrium is responsible for the initial growth of the signal amplitude when FT-EPR spectra are measured as a function of delay time between laser excitation and pi/2 microwave pulse. Also, it is found that Delta v(1/2)approximate to 1/pi T-m in both solvents over the whole temperature range. This establishes that there is a negligible contribution to the line width from unresolved C-13 hyperfine structure. The contribution of the electron spin-spin interaction modulated by rotational motion to the relaxation rates is analyzed. The analysis shows that the value of the zero-field splitting parameter D, which determines the magnitude of this contribution, is about an order of magnitude less than that found in rigid matrices at low temperature. A significant residual, temperature-independent, relaxation contribution is found which may stem from the rapid interconversion between triplet states that causes the reduction in D upon going from solid state to liquid solution.