We evaluate the small-amplitude excitations of a spin-polarized vapour of F
ermi atoms confined inside a harmonic trap. The dispersion law omega = omeg
a f[l + 4n(n + l + 2)/3](1/2) is Obtained for the vapour in the collisional
regime inside a spherical trap of frequency omega(f), with n the number of
radial nodes and l the orbital angular momentum. The low-energy excitation
s are also treated in the case of an axially symmetric harmonic confinement
. The collisionless regime is discussed with main reference to a Landau-Bol
tzmann equation for the Wigner distribution function: this equation is solv
ed within a variational approach allowing an account of non-linearities. A
comparative discussion of the eigenmodes of oscillation for confined Fermi
and Bose vapours is presented in an Appendix.