  We discuss the ground state and the small-amplitude excitations of dilute
boson-fermion mixtures confined in spherical harmonic traps at $T = 0$,
assuming repulsive boson-boson interactions and with each component being in a
single hyperfine state. From previous studies of the equilibrium density
profiles we propose a schematic phase diagram in a plane defined by the
variables $a_{bf}/a_{bb}$ and $a_{bb}k_f^{(0)}$, where $a_{bb}$ and $a_{bf}$
are the boson-boson and boson-fermion scattering lengths and $k_f^{(0)}$ is the
Fermi wave number at the centre of the trap. With this background we turn to
the equations of motion for density fluctuations in the collisional regime and
discuss some general features of the eigenmodes. We display analytic solutions
for sound waves in a quasi-homogeneous mixture and for surface modes at weak
fermion-boson coupling.
