The present paper reports the results of a systematic rheological study of the dynamic moduli of 1-butyl 3-methylimidazolium tetrafluoroborate ([Bmim][BF4]), 1-butyl 3-methylimidazolium hexafluorophosphate ([Bmim][PF6]), and 1-ethyl 3-methylimidazolium ethylsulfate ([Emim][EtSO4]) in the vicinity of their respective glass transition temperatures. The results show an anomalous aging in that the dynamic and the low shear rate viscosities decrease with time at temperatures near to, but above, the glass transition temperature, and this is described. The samples that are aged into equilibrium obey the time-temperature superposition principle, and the shift factors and the viscosities follow classic super-Arrhenius behaviors with intermediate fragility values as the glass transition is approached. Similar experiments using a high-purity [Bmim][BF4] show that using a higher purity of the ionic liquid, while changing absolute values of the properties, does not eliminate the anomalous aging response. The data are also analyzed in a fashion similar to that used for polymer melts, and we find that these ionic liquids do not follow, for example, the Cox-Merz relationship between the steady shear viscosity and the dynamic viscosity.