Abstract: The extraordinary structures and properties of fullerenes have had an important impact on nanotechnology as these compounds exhibit outstanding mechanical and electronic properties. 1,3-Dipolar cycloadditions (1,3-DCs) have proved to be a powerful way to functionalize these conjugated ? systems and have offered wide opportunities for the creation of new nanocarbon structures with potential application in biological, biotechnology, material science and medicinal chemistry. The 1,3-DCs of fullerene (C60) with nitrile oxides, RCNO, have been studied in the gas phase using density functional theory (DFT) at the B3LYP/6-31G(d) level. Energetic and kinetic parameters have been determined at room temperature so as to investigate the effect of electron-withdrawing (R = F, Cl, Br, NC, CN and NO2) and electron-releasing (R = Me and Et) substituents attached to the nitrile oxides on the 1,3-DCs. These parameters have been interpreted in terms of group electronegativity and DFT reactivity indices. An unexpected behaviour was observed for the 1,3-DC involving FCNO as these reactions have some pseudodiradical character. Inspired by the results of the 1,3-DCs of nitrile oxides to C60, we have extended this theoretical gas phase research to the addition of a second HCNO to the cycloadduct of the addition of HCNO on C60. The various possibilities for the second addition are being explored with the aim of determining the thermodynamic and kinetic products. The findings of our research should be helpful to experimentalists in their quests for functionalized fullerenes.