  We discuss causes of the formation of the observed kinematics and morphology
of cones of ionized matter in the neighborhood of the nuclei of Seyfert
galaxies. The results of linear stability analysis of an optically thin conic
jet where radiation cooling and gravity play an important part are reported.
The allowance for radiation cooling is shown to result in strong damping of all
acoustic modes and to have insignificant effect on unstable surface
Kelvin--Helmholtz modes. In the case of waveguide--resonance internal gravity
modes radiative cooling suppresses completely the instability of waves
propagating away from the ejection source and, vice versa, reduces
substantially the growth time scale of unstable sourceward propagating modes.
The results obtained can be used to study ionization cones in Seyfert galaxies
with radio jets. In particular, our analysis shows that surface
Kelvin--Helmholtz modes and volume harmonics are capable of producing regular
features observed in optical emission-line images of such galaxies.
