The stability of the MHD tangential discontinuity is studied in compressible
plasmas in the presence of anisotropic viscosity and thermal conductivity.
The general dispersion equation is derived and solutions to this dispersion
equation and stability criteria are obtained for the limiting cases of
incompressible and cold plasmas. In these two limiting cases the effect of
thermal conductivity vanishes and the solutions are only influenced by
viscosity. The stability criteria for viscous plasmas are compared with
those for ideal plasmas where stability is determined by the Kelvin-Helmholtz
velocity V_{KH} as a threshold for the difference in the equilibrium
velocities. Viscosity turns out to have a destabilizing influence when the
viscosity coefficient takes different values at the two sides of the
discontinuity. Viscosity lowers the threshold velocity V_c below the ideal
Kelvin-Helmholtz velocity V_{KH}, so that there is a range of velocities
between V_c and V_{KH} where the overstability is of a dissipative
nature.