Electron spin resonance (ESR) measurements including spin susceptibility, line width, and g value are given for M3C60 nominal compositions where M is an alkali metal. During about 24 h following the alkali-metal doping, the ESR signal of Rb3C60 is found to be time dependent in the temperature range 4-290 K. At room temperature, the same time dependence is also found in K3C60 and Cs3C60 but not in Na3C60, which is not superconducting. This time dependence of the ESR signal at room temperature appears to correlate with the development of a superconducting phase in K3C60 and Rb3C60 at lower temperature. The ESR line width 24 h after doping scales with the size of the crystal unit cell of M3C60. For Rb3C60 the temperature dependence of the ESR susceptibility, after 1 day or more, indicates a transition from an antiferromagnetic to a paramagnetic state around the superconducting transition temperature.