The constitutive equation used to characterize and model spinal tissues can significantly influence the conclusions from experimental and computational studies. Therefore, researchers must make critical judgments regarding the balance of computational efficiency and predictive accuracy necessary for their purposes. The objective of this study is to quantitatively compare the fitting and prediction accuracy of linear viscoelastic (LV), quasi-linear viscoelastic (QLV), and (fully) nonlinear viscoelastic (NLV) modeling of spinal-cord-pia-arachnoid-construct (SCPC), isolated cord parenchyma, and isolated pia-arachnoid-complex (PAC) mechanics in order to better inform these judgements. Experimental data collected during dynamic cyclic testing of each tissue condition were used to fit each viscoelastic formulation. These fitted models were then used to predict independent experimental data from stress-relaxation testing. Relative fitting accuracy was found not to directly reflect relative predictive accuracy, emphasizing the need for material model validation through predictions of independent data. For the SCPC and isolated cord, the NLV formulation best predicted the mechanical response to arbitrary loading conditions, but required significantly greater computational run time. The mechanical response of the PAC under arbitrary loading conditions was best predicted by the QLV formulation.