A previously-developed constitutive equation for nonlinear viscoelastic materials is first used to characterize mathematically the ply-level stress-strain behavior of a rubber-toughened carbon/epoxy composite. Emphasized are some practical aspects of carrying out such a characterization. Constant stress rate tests are used to derive first-loading material response in the dry state, at room temperature. It is found for a large portion of the loading curve that the shear and transverse compliances can be described by a quasi-elastic model expressed in terms of a single scalar function of stress state, a ratio of compliances, a time or rate exponent, and two elastic terms. This model offers a simple way to incorporate nonlinearity and time dependence in a material model for limited loading conditions. Results are then compared to those for a glass/epoxy composite with the same rubber-toughened resin system. Special considerations for using off-axis coupons are examined and unique tabbing is employed to derive material properties out to high stress levels. The consistency of the carbon/epoxy characterization is checked by comparing experimental stress-strain response to results not used in the characterization. Behavior of the two composite systems is compared and checked for consistency using a micromechanical model.