We have investigated the role that representative nonequilibrium carbon nanotube (CNT) network structures play in the flow-induced property changes of relatively high aspect ratio CNT/isotactic polypropylene (iPP) nanocomposites. Stable CNT network can form in CNT/iPP nanocomposites at relatively low CNT contents due to the employment of high aspect ratio CNTs. As experimentally demonstrated and theoretically predicted by Kharchenko et al. (Nat. Mater., 2004), large apparent negative normal stress differences (ΔN) might occur in long CNT systems under some particular conditions, for example, which satisfy the condition that the CNT network is strong enough to accommodate appreciable rotational distortion. In this study, we focused on the measurements of normal stress differences to explore the particular conditions for appearance of negative ΔN. We find that the values of ΔN are immensely influenced by initial normal stresses induced by squeezing deformation during the sample loading. Large negative ΔN can be observed under the subsequent shear flow with zeroing the initial normal stresses in our high aspect ratio CNT/iPP nanocomposites only if the CNT content is above the CNT gelation concentration, which is consistent with the previous studies of Kharchenko et al. This interesting result about the measurements of ΔN is further confirmed by a die-shrinkage extrusion behavior and at the same time the effect of shape-distortion instability in the extrusion of neat iPP can be diminished in the CNT/iPP nanocomposites.