In dynamic experiments using a highly sensitive torsion technique, the magnetic properties of the doped Rb3C60 single crystal are studied over a wide temperature range. The critical temperature of the superconducting transition Tc, the critical magnetic field Hc1, the pinning forces of both the Abrikosov vortices and the magnetic moments of dipoles at T >> Tc, at which relaxation processes are important, are determined and investigated. It was shown that the structural transition Fm3m-Pa3 at T = 260 K is accompanied by a reformation of the magnetic structure. Both the usual peaks at T ∼ 160–250 K and the not quite ordinary peaks of gigantic absorption of the energy of the oscillations, which shift to room temperature over time, were observed. The phenomenon is discussed in the framework of the cooperative Jahn-Teller effect, taking into account possible orbital and spin ordering. The relaxation processes at room temperatures (T ∼ 300 K) were studied. After many days of exposure (annealing) of fullerene at T ≥ 40 °C, in experiments with cooling from room temperatures, phenomena typical for a superconducting transition with giant pinning and damped oscillations were observed at T ∼ 200 K. The results of studies of magnetic phase transitions at T = 180–200 K in pure fullerite C60 (99.98% Term. Sublimed), which are related to the detected unusual magnetic phenomena in fullerene Rb3C60, are presented.