We report simulations of water confined between two parallel flat (hydrophobic) walls separated by 10.95 Å. Our results are consistent with the possibility of a liquid-liquid phase transition separating two phases of different densities. The low-density liquid phase displays tetrahedral "ice-like" local ordering, while the highdensity liquid phase shows indications of a hexagonal layer structure similar to the quasi-2D ice forms recently found in simulations using the TIP4P potential.Amorphous solid water displays two distinct phases, low density amorphous ice (LDA) and high density amorphous ice (HDA) that transform into each other via a first order phase transition. 1 Recently, it has been proposed that the transition line between these known phases can be extrapolated to higher temperatures into the metastable liquid region of the phase diagram, raising the intriguing possibility of the coexistence of two liquid phases and of the existence of a second critical point in the metastable liquid. 2 This "liquid-liquid phase transition" scenario has been supported by computer simulations with various effective interaction potentials, specifically with the ST2, 2,3 TIP4P, 2,4 and the SPC/E 5 potentials. Also, it has been shown that simple lattice models of water 6 as well as simplified spherically symmetric soft core potentials 7 and mean field approaches 8 can display a liquid-liquid-phase transition. Experimental evidence for the existence of the second critical point is difficult to obtain, since the strong nucleation tendency in the region of the phase diagram, where the second critical point might be found, makes it impossible to keep water in the liquid state. 9 It is not clear whether the liquid-liquid phase transition occurs also for strongly confined water. Water in confined systems plays an important role in many biological and geological systems, 10,11 and methods have been developed to experimentally test the behavior of molecularly thin water films confined between hydrophilic 12,13 as well as hydrophobic 14 and metal 15 surfaces. In some of these systems the freezing of water seems inhibited, 14,16 thus allowing one to study the phase diagram of water in regions not accessible for bulk water.Apart from a few recent studies, 17,18 computer simulations of confined water have mostly been done at ambient temperatures. [19][20][21][22] Here we use the Monte Carlo method to study strongly confined supercooled ST2 water. Our results are consistent with the possibility that a liquid-liquid phase transition occurs for similar temperatures and pressures as for the bulk. Further, we find that the anisotropy of the confined system plays a key role in determining the phase behavior. In constant density simulations, phase transition behavior can be found only for the lateral pressure P xy (parallel to the walls), not for the transverse pressure P z (perpendicular to the walls).Our system consists of N ) 216 water molecules interacting with each other via the ST2 potential, 23 and interacting with the walls via the...