To uncover the processes and mechanisms of cellular physiology, it first necessary to gain an understanding of the underlying metabolic dynamics. Recent studies using a constraint-based approach succeeded in predicting the steady states of cellular metabolic systems by utilizing conserved quantities in the metabolic networks such as carriers such as ATP/ADP as an energy carrier or NADH/NAD+ as a hydrogen carrier. Although such conservation quantities restrict not only the steady state but also the dynamics themselves, the latter aspect has not yet been completely understood. Here, to study the dynamics of metabolic systems, we propose adopting a carrier cycling cascade (CCC), which includes the dynamics of both substrates and carriers, a commonly observed motif in metabolic systems such as the glycolytic and fermentation pathways. We demonstrate that the conservation laws lead to the jamming of the flux and feedback. The CCC can show slow relaxation, with a longer timescale than that of elementary reactions, and is accompanied by both robustness against small environmental fluctuations and responsiveness against large environmental changes. Moreover, the CCC demonstrates robustness against internal fluctuations due to the feedback based on the moiety conservation. We identified the key parameters underlying the robustness of this model against external and internal fluctuations and estimated it in several metabolic systems.