Equilibrium and nonequilibrium solvation dynamics for a diatomic dipolar solute in water are studied via molecular dynamics (MD) computer simulations. The solute electronic structure;variation and associated polarizability are effected by a two-state description. This allows the instantaneous readjustment of the solute dipole moment to the fluctuating solvent environment. It is found that the solute polarizability has several striking consequences for solvation. Both inertial and diffusive solvation dynamics become significantly slower as the solute polarizability increases; the relative contribution to overall solvation from the inertial dynamics becomes markedly;reduced, Another novel feature is that the dynamics along the Franck-Condon energy gap coordinate-widely employed in many MD studies of solvation-become dependent on the relative dipole character of the ground and excited electronic states, as well as on their relative polarizability difference. It is also found that the validity of Linear response becomes considerably limited when the solute is polarizable.