The structure and dynamics of water confined in model single-wall carbon- and boron-nitride nanotubes (called SWCNT and SWBNNT, respectively) of different diameters have been investigated by molecular dynamics (MD) simulations at room temperature. The simulations were performed on periodically extended nanotubes filled with an amount of water that was determined by soaking a section of the nanotube in a water box in an NpT simulation (1 atm, 298 K). All MD production simulations were performed in the canonical (NVT) ensemble at a temperature of 298 K. Water was described by the extended simple point charge (SPC/E) model. The wall-water interactions were varied, within reasonable limits, to study the effect of a modified hydrophobicity of the pore walls. We report distribution functions for the water in the tubes in spherical and cylindrical coordinates and then look at the single-molecule dynamics, in particular self-diffusion. While this motion is slowed down in narrow tubes, in keeping with previous findings (Liu et al. J. Chem. Phys. 2005, 123, 234701-234707; Liu and Wang. Phys. Rev. 2005, 72, 085420/1-085420/4; Liu et a]. Langmuir 2005, 21, 12025-12030) bulk-water like self-diffusion coefficients are found in wider tubes, more or less independently of the wall-water interaction. There may, however, be an anomaly in the self-diffusion for the SWBNNT.