A series of polymer/clay nanocomposites containing mechanistically two different polymers, poly(ethylene glycol) (PEG) and poly(epsilon caprolactone) (PCL), were prepared by simultaneous copper(I)-catalyzed alkyne-azide cycloaddition click reactions. Both clickable polymers, PEG-Alkyne and PCL-Alkyne, were simultaneously clicked on to azide-functional montmorillonite (MMT-N-3) nanoclay to get corresponding PEG-PCL/MMT nanocomposites. The chemical structures of the resulting nanocomposites were verified by following azide and silicone-oxygen bands using FT-IR and characteristic bands of PEG and PCL segments using H-1-NMR spectroscopy. The combined XRD and TEM analysis confirmed that all PEG-PCL/MMT nanocomposites had partially exfoliated/intercalated morphologies. In addition, the increase of MMT-N-3 loading not only improved the onset and maximum degradation temperatures of the nanocomposites but also their char yields. Furthermore, the incorporation of MMT-N-3 in the polymer matrix did not significantly influence the crystallization behavior of both PEG and PCL segments.