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