Mechanical fatigue under strain controlled tension/tension (T/T) of rectangular un-notched and notched specimens of high density polyethylene and polyamide 6 was performed. Under large amplitude oscillatory elongation, the stress response is nonlinear asymmetric due to a different stress response during loading and unloading and was analyzed via discrete Fourier transform. Dynamic strain (epsilon(0)) sweep tests revealed odd (I-3/1 alpha epsilon(2)(0)) and even (I-2/1 alpha epsilon(1)(0)) harmonics in the stress, well described by the Neo-Hooke's law. Before crack onset for the Nc specimens, the storage and loss moduli and I-2/1 are constant, but I-3/1 increases with fatigue. The first derivative of I-3/1 (dI(3/1)/dN) and the cumulative nonlinearity Q(f) parameter (integral of I-3/1/epsilon(2)(0)) were found to be strong criteria predicting fatigue. To break the unnotched specimens in the low and high cycle fatigue regime, large strain amplitudes were applied, resulting for both materials in initial plastic deformation followed by buckling when a critical compression force is exceeded. This results in a different time evolution of the linear and nonlinear parameters, especially as a minimum in the I-2/1 curve. Finally, a model is proposed to describe the nonlinear viscoelastic specimen response under T/T and the effect of buckling.