- The instability of a Fermi-liquid drop with respect to bulk density distortions is considered. It is shown that the presence of the surface strongly reduces the growth rate of the bulk instability of the finite Fermi-liquid drop because of the anomalous dispersion term in the dispersion relation. The instability growth rate is reduced due to the Fermi-surface distortions and the relaxation processes. The dependence of the bulk instability on the multipolarity of the particle density fluctuations is demonstrated for two nuclei 40Ca and 208Pb. It is shown that the formation of the decay modes (fission or multifragmentation) of an unstable Fermi-liquid drop depends on the location of the radial wave number q on the slopes of the instability growth rate (g) and is different for both nuclei 40Ca and 208Pb.