The first normal stress difference (N1) behavior of polymer nanocomposites and liquid crystalline polymer (LCP) composites is a measure of elasticity and is affected by shear stress as a result of morphological alterations at the molecular and nanostructure levels. In this study, the steady shear rheological behaviors of polylactide (PLA) and nanographite platelet (NGP) bionanocomposites containing 1, 2, 3, and 5 wt% nanofiller were investigated. The shear rheological properties of glass fiber-filled LCPs (filler aspect ratio>100) were also examined. One of the objectives of this study was to obtain a correlation between N1, filler contents, and shear stress/rate of the measurements. The results suggest that N1 in PLA/NGP bionanocomposites is dependent on the level of filler loading as well as the shear rate beyond a critical value. For the LCP systems, N1 is positive for the unfilled and negative for the glass fiber-filled LCPs, respectively. A novel rectangular hyperbola model was successfully developed and utilized to fit the N1 data of the neat PLA and PLA/NGP composites as well as the unfilled LCPs. The anomalous N1 behavior of PLA/NGP and LCP composites was also thoroughly discussed in this study. POLYM. ENG. SCI., 54:1300-1312, 2014.