Frequency response behavior of the constant molar flow semi-batch adsorption vessel containing coreshell composites is theoretically investigated. The periodic modulation of the inlet molar flow-rate into the vessel is considered as the forcing function to the response. Under the interaction between the core-phase and the shell-phase of the composite, both the response of the core-phase and the response of the shell-phase subject to the forcing function exhibit their own peaks on the out-of-phase characteristic curve and their own plateaus on the in-phase characteristic curve, respectively. The model to be developed will include the local linear equilibriums at the fluid-particle interface and at the intraparticle core-shell interface, the external diffusion, the intraparticle diffusion in the outer shell-phase, and the intraparticle diffusion in the inner core-phase.