Carbon nanotube (CNT)/Natural rubber (NR)/ ethylene–propylene diene monomer (EPDM) nanocomposites were prepared via a traditional mixing method using a two‐roll mixer and cured by a conventional vulcanization system. The nanocomposites were characterized with respect to their curing characteristics and mechanical properties. The cure characteristic investigations showed that the introduction of CNTs into the rubber blend leads to a decrease in scorch and cure times. The minimum and maximum torque values of the cured nanocomposites rise with respect to CNTs loading. Tensile strength of NR/EPDM (75/25 wt/wt) blends containing 0.5 wt% of CNTs showed an increase compared to the NR/EPDM blends. The moduli of the nanocomposites at 100% and 300% elongations revealed that the CNTs can increase these parameters with no significant effect on the elongation at break. The stress–strain behavior of the nanocomposites was analyzed by some proper phenomenological hyperelastic models and the effect of CNTs loading on their material parameters was investigated. The introduction of CNTs into the NR/EPDM matrix leads to a significant change in material parameters of hyperelastic models. The results suggested that various CNTs loadings have a significant effect on the dispersion state of nanotubes and ultimate mechanical properties of CNT/NR/EPDM nanocomposites. POLYM. COMPOS., 39:4071–4079, 2018. © 2017 Society of Plastics Engineers