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Structural dynamics in the glassy state of two protic ionic liquids, carvedilol phosphate and procaine hydrochloride, were characterized from analysis of changes in the conductivity relaxation times during physical aging. The obtained relaxation times, having a magnitude exceeding feasible experimental time scales and thus not directly measurable, are consistent with published data from a method that relies on the presence of a secondary relaxation. We also observe a narrowing of the relaxation dispersion, specific to higher frequencies, that is a consequence of the heterogeneous dynamics of deeply supercooled materials.