We report results from molecular dynamics simulations of the freezing and melting, at ambient temperature (T=300 K), of a bilayer of liquid water induced by either changing the distance between two confining parallel walls at constant lateral pressure or by lateral compression at constant plate separation. Both transitions are found to be first order. The system studied consisted of 1200 water molecules that were described by the TIP5P model. The in-plane symmetry of the oxygen atoms in the ice bilayer was found to be rhombic with a distorted in-registry arrangement. Above and below the stability region of the ice bilayer we observed two bilayer phases of liquid water that differ in the local ordering at the level of the second shell of nearest neighbors and in the density profile normal to the plane, yielding two liquid phases with different densities. These results suggest the intriguing possibility of a liquid-liquid transition of water, confined to a bilayer, at regions where the ice bilayer is unstable with respect to either of the liquid phases. In addition, we find that under the same conditions, water confined to 3-8 layers remains in the liquid phase (albeit stratification of the transverse density profile) with values of the lateral diffusion coefficient comparable to that of the bulk. (C) 2003 American Institute of Physics.