The aim of the present study has been to evaluate the effect of hybridization of montmorillonite (MMT) and multi-walled carbon nanotubes (MWCNT) on the thermal and viscoelastic properties of shape memory epoxy polymer (SMEP) nanocomposites. In this study, ultra-sonication was utilized to disperse 1%, 3%, and 5% MMT in combination with 0.5%, 1%, and 1.5% MWCNT into the epoxy system. The fabricated SMEP hybrid nanocomposites were characterized via differential scanning calorimetry, dynamic mechanical analysis, and thermogravimetric analysis. The storage modulus (E’), loss modulus (E”), tan δ, decomposition temperature, and decomposition rate, varied upon the addition of the fillers. Tan δ indicated a reduction of glass transition temperature (Tg) for all the hybrid SMEP nanocomposites. 3% MMT/1% MWCNT displayed best overall performance compared to other hybrid filler concentrations and indicated a better mechanical property compared to neat SMEP. These findings open a way to develop novel high-performance composites for various potential applications, such as morphing structures and actuators, as well as biomedical devices.