The stability of C60 and C70 fullerenes in the interstellar medium deposited on dust surface or embedded in meteorites and comets has been simulated with γ irradiation and with He+ ion bombardment. It is shown by vibrational spectroscopy that a γ radiation dose of 2.6MGy (1Gy = 1 joule absorbed energy per kilogram) causes partial oligomerization of both C60 and C70 fullerenes. Oligomers are made by fullerene cages chemically connected each other which can yield back free fullerenes by a thermal treatment. The amount of irreversibly polymerized fullerenes caused by 2.6MGy as deduced as the toluene insoluble fraction has been determined as 1.7 and 15 per cent by weight, respectively, for C60 and C70 fullerene. The radiation dose generated by radionuclides decay and expected to be delivered to fullerenes buried at a depth of more than 20m in comets and meteorites is about 3MGy per 109yr. Since fullerenes are by far resistant to such radiation dose they can survive for at least some billion years inside comets and meteorites and in fact have been detected inside certain carbonaceous chondrites. On the other hand, the direct exposure of fullerenes to cosmic rays for instance when they are adsorbed or deposited on the surface of carbon dust corresponds to the delivery of a radiation dose comprised between 30 and 65MGy per 109yr. Experimental bombardment of both C60 and C70 fullerenes for instance with He+ ions has shown that the complete amorphization occurs at about 250MGy. Thus in ~4 Gyr exposure to cosmic rays it is expected a complete amorphization.