The character of some free radical in pure C-60 and a mixture of C-60 and C-70 was studied by means of ESR spectroscopy. The experiment results show that the ESR signals of the free ridical in C-60 or the mixture of C-60 and C-70 are dependent on oxygen and the ratio between C-60 and C-70. The radical in pure C-60 and the mixture of C-60 and C-70 possess the characteristic of carbon-centered radicals.