The linear stability of the plasma tail of a comet is numerically investigated. The zeroth-order model of the tail plasma configuration is based on the result of a companion paper (Malara et al., this issue), discussing the possible modeling of the data obtained during the ICE encounter with comet Giacobini-Zinner. Effects both of finite resistivity and of velocity shear are taken into account. The tail appears to be unstable against Kelvin-Helmholtz-like modes in which a certain amount of reconnection occurs. Because of the velocity flow shear the perturbation extends far beyond the singular layer and affects in depth the magnetic lobes. The relative importance of the Kelvin-Helmoltz turbulence in the lobes and the level of reconnection, the typical wavelengths, and the growth time of the mode depend on the particular cometary tail considered. ¿ American Geophysical Union 1989