This work was aimed at contrasting the properties of water near highly hydrophilic or highly hydrophobic walls. We performed molecular dynamics computer simulations of two systems, both composed of a number of water molecules together with a layer of either purely hydrophilic or purely hydrophobic molecules restrained in mobility so as to form walls. Simulations were done at constant temperature and at constant volume or constant pressure. We found that the hydrophilic wall induces strong ordering near its surface, but such order is present only up to about two molecular diameters away from it. On the other hand, the hydrophobic wall induces a slight ordering, but this ordering remains for several molecular diameters inside the bulk.