We present measurements of induced absorption and its dynamics in C60-doped solid xerogel matrices. The measurements are performed in a pump-test geometry using picosecond pulses generated from a frequency doubled mode locked Nd:YAG laser at 532 nm. We observe an induced absorption leading to optical limiting. We find outstanding optical limiting qualities for single shot excitation but some degradation above a certain threshold intensity for repetitive pulses. Below this degradation threshold, the material is stable and its limiting dynamics is studied. A decrease of the initial laser-induced absorption with a time constant of 150 ps is observed, down to a very long-lived constant level. We attribute this dynamics of induced absorption to a transition from excited singlet to triplet electronic states in the C60 molecule.