The thermal behavior of graphite, C-60 fullerene, fullerene black (carbon soot containing fullerenes), extracted fullerene black and diamond has been analyzed to 1000degreesC by TGA-DTA (thermogravimetric analysis and differential thermal analysis) under a nitrogen flow at a heating rate of 20degreesC/min. Very small weight losses have been recorded in the case of graphite and-diamond. Furthermore no diamond graphitization has been observed. The sublimation of pure C-60 and the fullerene fraction of fullerene black (both pristine and extracted) has been observed and discussed. The combustion reaction in air flow of graphite, C-60 and C-70 fullerenes, fullerene black (both unextracted and extracted), carbon nanotubes and diamond has been studied by TGA-DTA at a heating rate of 20degreesC/min. C-70 fullerene and fullerene black have been found to be the most reactive carbon materials with O-2. The role played by C-70 in the degradation of fullerites has been discussed. Among the carbon materials examined, the best resistance to O-2 attack has been shown by diamond and carbon nanotubes. The behavior of graphite is intermediate between diamond and fullerene blacks. The behavior of C-60 fullerene appears closer to that of graphite although it appears to be more reactive with O-2. Samples of graphite and carbon blacks N375 and N234 have been studied by TGA-DTA in air flow before and after a radiation treatment with neutrons or gamma radiation. The effect of the radiation damage in the combustion reaction of these carbon materials has been discussed.