The results from a numerical investigation of the dependence of the eigenfrequency and structure of Alfv¿nic field line resonance (FLR) layers on the dispersion of the resonant Alfv¿n waves are presented. The investigation is based on the linear, reduced, two-fluid MHD-kinetic model considered in the dipole magnetic field geometry with a realistic distribution of the background plasma parameters along the entire auroral flux tube. It is shown that (1) dispersion of the small-scale Alfv¿n wave due to the finite electron inertia (inertial dispersions) decreases the eigenfrequency of the Alfv¿nic FLR and broadens the FLR layer in the direction along the transverse gradient in the background Alfv¿n speed; (2) dispersion of the wave due to the finite plasma temperature (kinetic dispersion) increases the FLR eigenfrequency and broadens the resonance layer in the opposite direction; and (3) on the field line where the effect of the kinetic dispersion balances the effect of the inertial dispersion, the eigenfrequency becomes independent of the transverse wavelength of the resonant wave. As a result, a FLR occurring on such a particular field line develops fields and currents with smaller transverse scale sizes and larger amplitudes than FLRs on field lines where inertial and kinetic dispersions are not in a balance. ¿ 1999 American Geophysical Union