Large amplitude oscillatory shear (LAOS) is a useful tool for the study of nonlinear viscoelasticity in polymeric liquids. To concisely describe the response of a material to such a test, it is desirable to make use of a constitutive equation. In this way, the response can be described in terms of the parameters of the rheological model. We have found a separable BKZ model, e.g., Wagner’s equation, to be useful in this regard for LDPE IUPAC X. The damping function determined in step shear experiments does not lead to accurate predictions of the LAOS response. For a given low frequency, however, it is possible to fit the parameters of a simple damping function equation to the LAOS response at one strain amplitude and to use these parameter values to reliably predict the response at other strain amplitudes. Thus, the Wagner equation provides a basis for the concise description of the response of LDPE IUPAC X to large amplitude oscillatory shear experiments at low frequencies. Conversely, it was found that the response of a HDPE melt to large amplitude oscillatory shear cannot be concisely described by the Wagner equation.