It is well accepted that due to epitaxy matching, carbon nanotubes are good nucleatingagent for linear polyethylene. We demonstrate that not only in the quiescent conditionsbut also at the relatively low shear rates the presence of single-walled carbon nanotube(SWCNT) accelerates the crystallization kinetics of polyethylene (PE). The influence ofSWCNTs on the crystallization kinetics in the quiescent condition is followed with the helpof rheological and differential scanning calorimetry studies. The influence of flow on thestretch of the polymer chain is probed using time-resolved small-angle X-ray scattering(SAXS) and is verified with the Deborah number. SAXS data indicates that the strong shearingconditions (shear rate > 50/s for 1 s) are requisite to form shish-kebab structure in theneat polymer. However, for the low shear (shear rate <50/s for 1 s), the shish-kebab structurethat arises due to chain orientation is enhanced in the presence of SWCNTs. Thedevelopment of oriented structures in SWCNT/PE composites and their absence in the neatpolymer under low shear rate indicates that the presence of SWCNTs plays a significantrole in the chain orientation. Overall, the results manifest the influence of SWCNTs onchain relaxation of the polymer.