Medium-amplitude oscillatory shear experiments are employed to study the supramolecular relaxation modes in hydroxyl terminated polydimethylsiloxane. For these associating melts, this allowed us to identify the nonlinear rheological signature of hydrogen bond-mediated structures occurring in addition to those of the covalent chains. First-order and third-order nonlinearity parameters are determined for the supramolecular and chainlike modes to compare them with the predictions of an array of rheological models. Fingerprints of the two supramolecular modes can be recognized in the nonlinear response. By collecting third-order nonlinearity parameters (3)Q(0) for about 35 materials including polymer melts, polymer solutions, and other viscoelastic fluids, it is demonstrated that the maximum value of (3)Q(0) correlates with the magnitude of the shear modulus at the frequency at which this maximum occurs. The implications of this experimental finding are discussed.