Employing theory derived in previous papers [Meng and Russel, Macromolecules 36, 10112-10119 (2003); 38, 593-600 (2005)] to describe the micellar structure of aqueous solutions of telechelic polymers with a poly(ethylene oxide) (PEO) backbone and alkane end groups, we predict the high-frequency modulus and low shear viscosity for comparison with data from the literature and our own experiments. In these solutions the molecular structure determines the aggregation number and radius of the micelles. Interactions between micelles lead to exchange of end blocks and compression of loops, generating a pair potential with an attractive well and soft core. Computing the high-frequency modulus from the intermicellar potential and constructing a correlation for the relaxation time from experimental data allows us to predict the low shear viscosity. Comparison with measurements for our model associative polymers, as well as relatively monodisperse systems from the conventional synthesis, suggests an alternative to the structure-property relations constructed by Annable et al., J. Rheol. 37, 695 (1993) by modifying reversible network theory. The distinctions lie in our incorporation of excluded volume repulsions and entropic attractions between micelles, which produce strong correlations that determine the concentration dependence. (c) 2006 The Society of Rheology.