Different ultraviolet (UV) and infrared (IR) auroral features have been observed at Jupiter and Saturn. Using models related to UV and IR auroral emissions, we estimate the characteristic time scales for the emissions, and evaluate whether the observed differences between UV and IR emissions can be understood by the differences in the emission time scales. Based on the model results, the UV aurora at Jupiter and Saturn is directly related to excitation by auroral electrons that impact molecular H2, occurring over a time scale of 0.01 sec. The IR auroral emission involves several time scales: while the auroral ionization process and IR transitions occur over < 0.01 sec, the time scale for ion chemistry is much longer at 0.01-10000 sec. Associated atmospheric phenomena such as temperature variations and circulation are effective over time scales of > 10000 sec. That is, for events that have a time scale of ~100 sec, the ion chemistry, present in the IR but absent in the UV emission process, could play a key role in producing a different features at the two wavelengths. Applying these results to the observed Jovian polar UV intensification events and the Io footprint aurora indicates that whether the IR intensity varies in correlation with the UV or not depends on the number flux of electrons and their characteristic energy.