Supramolecular gels are three-dimensional network structures formed by the hierarchical self-assembly of small molecules through weak noncovalent interactions. On the basis of the various interactions contributed by specific functional groups/moieties, gels with different architectures can be constructed that are smart to the external stimuli such as pH, type of solvent, stress, temperature, etc. In the present work, we explore the oscillatory shear response of supramolecular self-assembled systems formed by the low-molecular-weight (LMW) gelator based on difunctionalized amino acid, florenylmethoxycarbonyl (Fmoc)-lysine(Fmoc), Fm-K(Fm) in aqueous buffer solution, at two different pH (6 and 7.4). Small amplitude oscillatory shear (SAOS) reported weak frequency dependence of moduli indicating a gel-like network structure. Large amplitude oscillatory shear (LAOS) indicated flow regimes dictated by yielding and subsequent network dynamics analogous to cagelike soft glassy events reported for colloidal systems. The three interval thixotropy test (3iTT) indicated recovery of moduli due to regelation contributed by the reversible interactions. A generalized network model framework is utilized to investigate the transient network characteristics of the Fm-K(Fm) gels. The "network creation" and "network loss" rates were chosen as exponential functions of scaled shear stress (= ) to effectively describe the complex response. On the basis of the insights, possible mechanisms to explain the differences/similarities in the response at different pH are speculated. It is further illustrated that the modeling strategy can be extended to supramolecular gels of different classes because of the commonality/universality of their response features under oscillatory shear.