The extended Lagrangian method is applied to a polarizable model for liquid water. The variables describing the polarization are treated as classical dynamical degrees of freedom equivalent to the configuration coordinates of the liquid. Two different optimization schemes are compared. In the first, the polarization fluctuations are in thermal equilibrium with the liquid. In the second, adiabatic conditions are imposed by cooling the polarization fluctuations and separating the time scale of the fictitious dynamics of the polarization from the physical motion of the liquid. The characteristic time of the response to a change in the configuration is controlled by scaling a mass parameter in the extended equations of motion. The temperature difference is maintained by Nose thermostats. Energies and structure are found to be relatively insensitive to the mode of optimization. Also the short-time dynamics of vibrations and librations is essentially independent of fictitious mass variations, provided the thermal polarization fluctuations have been suppressed. Relaxation processes such as diffusion and reorientation are strongly inhibited by both delayed response and too high temperature of the polarization. The solvation of a chlorine anion is also investigated. The hydration number and the adiabatically converged residence times are in good agreement with experiment. © 1991 American Chemical Society.