The first normal stress difference (N-1) in large amplitude oscillatory shear (LAOS) consists of two contributions: one from non-oscillating nonzero mean value and the other from oscillating even harmonics, while the nonlinear shear stress can be expressed as a sum of odd harmonics. In this study, the two nonlinear contributions of N-1 in entangled polymer solutions have been analyzed by systematical comparison with their shear stress counterparts (storage modulus and odd harmonics, respectively) as a function of strain amplitude and of Deborah number (De). The contributions of N-1 were greater than those of the shear stress in the LAOS region. The nonzero mean value of N-1 decreased with an increase in Deborah number, but conversely, the second harmonic of N-1 increased. The relative intensity (the second harmonic over the fourth harmonic of N-1) as an indicator of the nonlinearity of N-1 decreased with the Deborah number. We also compared experimental results to model predictions from the eight-mode Giesekus constitutive equation. For the model, we obtained two sets of nonlinear parameters from the best fit of model predictions with both steady shear viscosity and the first normal stress difference coefficient. The model could not quantitatively predict the first normal stress difference behavior in LAOS even with these nonlinear parameter sets, which fit the steady data very well. This study shows that the contribution of the first normal stress difference in LAOS is as vital as that of shear stress, and it can be used as a good estimate of the performance of the constitutive equation. (C) 2010 The Society of Rheology. [DOI: 10.1122/1.3483611]