We perform linear stability analysis of solvent density modes in the presence of nonpolar solute-solvent interaction in a nonpolar solvent. The dominant instability given by the maximum positive eigenvalue of the stability matrix provides the time scale of the solvent rearrangement around a solute. Our theory predicts two long time scales for both in normal nonpolar and supercritical fluids. We discuss the existing experimental results on nonpolar solvation dynamics in light of our prediction.