The spin wave stiffness constant D ((q) over cap) of unsupported Fee (
100), (110), and (111) nickel monolayers are calculated for different
directions, (q) over cap, of spin wave propagation. It is shown that D
is isotropic for the (100) and (111) orientations, and highly anisotr
opic for the (110) orientation. Results indicate that the strength of
the exchange coupling between nearest neighbour magnetic moments is qu
ite sensitive to the effective space dimensionality as well as the cry
stalline structure of the system.