Dynamic Stokes shift measurements of the solvatochromic probe trans-4-dimethylamino-4'-cyanostilbene were used to measure the solvation response of five imidazolium and one pyrrolidinium ionic liquid at 25 degrees C. The Kerr-gated emission and time-correlated single-photon-counting techniques were used to measure spectral dynamics occurring over the time ranges of 100 fs-200 ps and 50 ps-5 ns, respectively, and a combination of data sets from these two techniques enabled observation of the complete solvation response. Observed response functions were found to be biphasic, consisting of a sub-picosecond component of modest (10-20%) amplitude and a dominant slower component relaxing over times of a few picoseconds to several nanoseconds. The faster component could be correlated to inertial characteristics of the constituent ions, and the slower component to solvent viscosity. Dielectric continuum calculations of the sort previously used to predict solvation dynamics in dipolar liquids were shown to work poorly for predicting the response in these ionic liquids.