The reaction of fullerenes and carbon nanotubes with molecular fluorine has been studied using B3LYP calculations. The nanotube substrates are represented by model polycyclic aromatic hydrocarbons that are constrained to have nonplanar geometries with curvatures corresponding to (10,10), (5,5), and (16,0) nanotubes. Most of the calculations for fullerenes are carried out for C60. The calculations are focused on the addition of one to four F-atoms to the fullerene or nanotube substrate. The preferred binding sites for sequential fluorine addition are studied along with the geometry deformations experienced by the substrate. For C60, a strong preference exists for pairwise addition to the C−C double bonds between pentagons (denoted 6/6 addition). Subsequent addition to neighboring 6/6 bonds is also favored. These results are in agreement with recent experimental data. For addition of F2 to armchair nanotubes, the favored product has the fluorine atoms bonded to adjacent carbons with an orientation perpendicular to the tube axis, whereas for zigzag nanotubes the favored orientation is parallel to the tube axis. However, in the latter case a second product with the fluorine atoms at the 1−4 positions of a hexagon, but still parallel to the tube axis, is less than 0.8 kcal/mol higher in energy. The binding energy of a pair of fluorine atoms to C60 is 115 kcal/mol, which is greater than the value found for any of the nanotube model molecules. Zigzag nanotubes are found to form more stable fluorination products than armchair tubes of comparable diameter (83 kcal/mol for (16,0) compared to 76 kcal/mol for (10,10) for addition of F2). However, smaller diameter nanotubes such as the (5,5) armchair tube have even higher binding energies (91 kcal/mol for addition of F2). For C60 and (10,10) nanotubes, addition of a second F-atom pair results in higher binding energies per F-atom than is found for the first pair. Limited calculations have been carried out to estimate the energy barriers for the fluorination process.