Double-step strain flows with strain reversal provide critical tests of proposed constitutive equations for nonlinear viscoelasticity. In the present study, two rheological consistency relations that involve the relaxation of the first normal stress difference in reversing double-step strain flows are evaluated using a new experimental data set on a concentrated polystyrene solution. One consistency relation can be thought of as the double-step strain flow analog of the Lodge-Meissner relation for single-step strain flow. Osaki’s assertion on the validity of this consistency relation for a rather general class of fluids is verified by a formal proof given in the Appendix to this paper. The second consistency relation is valid for several well-known constitutive equations (i.e., K-BKZ and Doi-Edwards) falling within this general class of fluid behavior that give significantly different predictions for the shear stress in the same flow. The first consistency relation was satisfied by the system considered as was the Lodge-Meissner relation. The second consistency relation was not satisfied by the K-BKZ, Doi-Edwards, or strain coupling theories but was in qualitative agreement with Wagner’s irreversible network rupture theory.