Recently Berg and co-workers have reported interesting time resolved studies of ultrafast solvation dynamics in a completely nonpolar liquid. The relevant time correlation function was found to exhibit many fascinating properties. It was biphasic and highly nonexponential in the supercooled liquid near the glass transition temperature. In this article we present a general microscopic theory of such solvation phenomena. It is found that in contrast to solvation of charged species in polar solvents, the nonpolar solvation dynamics in controlled essentially by the dynamic structure factor of the liquid; the orientational relaxation is seen to play a less important role. As the dynamic structure factor shows anomalous behavior in the supercooled liquid, so does the solvation time correlation function. The theory suggests that nonpolar solvation dynamics can be an important scale dependent probe of microscopic dynamical processes in the supercooled liquid.