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Association between cations and anions plays an important role in the interfacial structure of room-temperature ionic liquids (ILs) and their electrochemical performance. Whereas great efforts have been devoted to investigating the association effect on the equilibrium properties of ILs, a molecular-level understanding of the charging dynamics is yet to be established. Here, we propose a theoretical procedure combining reaction kinetics and the modified Poisson-Nernst-Planck (MPNP) equations to study the influences of ionic association on the dynamics of electrical double layer (EDL) in response to an applied voltage. The ionic association introduces a new decay length λS and relaxation time scale τRC=λSL/D, where L is the system size and D is ion diffusivity, that are distinctively different those corresponding to non-associative systems. Analytical expressions have been obtained to reveal the quantitative relations between the dynamic timescales and the association strength.