The effect of several concentrations of carboxylated nitrile butadiene rubber (XNBR) functionalized halloysite nanotubes (XHNTs) on the vulcanization and degradation kinetics of XNBR/epoxy compounds were evaluated using experimental and theoretical methods. The isothermal vulcanization kinetics were studied at various temperatures by rheometry and differential scanning calorimetry (DSC). The results obtained indicated that the nth order model could not accurately predict the curing performance. However, the autocatalytic approach can be used to estimate the vulcanization reaction mechanism of XNBR/epoxy/XHNTs nanocomposites. The kinetic parameters related to the degradation of XNBR/epoxy/XHNTs nanocomposites were also assessed using thermogravimetric analysis (TGA). TGA measurements suggested that the grafted nanotubes strongly enhanced the thermal stability of the nanocomposite.