In an effort to gain insight into the activation energies and reaction enthalpies of the chemical functionalization of carbon and boron nitride nanotubes, calculations using density functional theory have been carried out for the cycloaddition of a heavy carbene to a single-walled carbon (SWCNT; C1(30)H(20)) and a boron nitride (SWBNNT; B65N65H20) nanotube. The (CH3)(2)X + SWCNT and (CH3)(2)X + SWBNNT (X = C, Si, Ge, Sn, and Pb) reactions are the subject of the present study. All the stationary points were determined at the B3LYP/LANL2DZ level of theory. The major conclusions that can be drawn from this work are as follows: (i) Considering both the activation barrier and reaction enthalpy based on the model calculations presented here, it is found that the order of (CH3)(2)X reactivity is X = C > Si >> Ge > Sn > Pb, irrespective of whether cycloaddition is to a SWCNT or a SWBNNT sidewall. That is to say, (CH3)(2)C and (CH3)(2)Si can readily add to the sidewalls of SWCNT and SWBNNT, whereas (CH3)(2)Ge, (CH3)(2)Sn, and (CH3)(2)Pb are unreactive. (ii) Since the chemical reactivities of SWCNT and SWBNNT sidewalls closely resemble those of the small C16H10 and B8N8H10 molecules, at least in a qualitative sense, the use of the above small molecules as models is sufficient to provide qualitatively correct results. (iii) Our theoretical observations indicate that all the (5,5) SWCNT and SWBNNT cycloadducts favor opened rather than closed three-membered ring structures. (iv) The theoretical investigations demonstrate that the singlet-triplet splitting of the carbene species (R2X) as well as that of the small model molecules can be used as a diagnostic tool to predict the addition reactivities of carbene analogues and sidewalls of various nanotubes, respectively. Moreover, the results obtained in this work allow a number of predictions to be made.