The influence of exposure to UV light and moisture on the durability of a multiwalled carbon nanotube(MWCNT)/epoxy nanocomposite was investigated. Samples of epoxy resin based on diglycidyl ether of bisphenol A (DGEBA) cured with 2,2,4-trimethylene-1,6-hexadiamine (TMDA), and epoxy nanocomposite containing 0.5% MWCNT were exposed to different accelerated weathering times between one and six months. Changes in surface chemistry, mechanical properties (tensile tests), thermal properties (thermogravimetric analysis and differential scanning calorimetry), and morphology were evaluated before and after exposure to accelerated weathering for a period of up to six months. Epoxy nanocomposite (DGEBA–TMDA/0.5%MWCNT) samples had improved thermal stability and resistance to degradation, compared to epoxy resin (DGEBA–TMDA). The effect of MWCNT at reducing degradation was more pronounced than previously found for resins prepared with hydrogenated DGEBA.