The propagation of the isoscalar and isovector sound modes in a hot nuclear
matter is considered. The approach is based on the collisional kinetic the
ory and takes into account the temperature and memory effects. It is shown
that the sound velocity and the attenuation coefficient are significantly i
nfluenced by the Fermi surface distortion (FSD). The corresponding influenc
e is much stronger for the isoscalar mode than for the isovector one. The m
emory effects cause a nonmonotonous behavior of the attenuation coefficient
as a function of the relaxation time leading to a zero-to-first sound tran
sition with increasing temperature. The mixing of both the isoscalar and th
e isovector sound modes in an asymmetric nuclear matter is evaluated. The c
ondition for the bulk instability and the instability growth rate in the pr
esence of the memory effects is studied. It is shown that both the FSD and
the relaxation processes lead to a shift of the maximum of the instability
growth rate to the longer-wavelength region.