The present study of the two-stream instability in stellar disks with
counterrotating components of stars and/or gas is stimulated by recent
ly discovered counterrotating spiral and SO galaxies. Strong linear tw
o-stream instability of tightly wrapped spiral waves is found for one-
and two-armed waves with the pattern angular speed of the unstable wa
ves always intermediate between the angular speed of the corotating ma
tter (+Omega) and that of the counterrotating matter (-Omega). The ins
tability arises from the interaction of positive and negative energy m
odes in the co- and counterrotating components. The unstable waves are
in general convective-they move in radius and radial wavenumber space
-with the result that amplification of the advected wave is more impor
tant than the local growth rate. For a galaxy of corotating stars and
counterrotating stars of mass fraction xi(g), < 1/2, or of counterrota
ting gas of mass fraction xi(g), < 1/2, the largest amplification is u
sually for the one-armed leading waves (with respect to the corotating
stars). For the case of both counterrotating stars and gas, the large
st amplifications are for xi + xi(g) approximate to 1/2, also for one
-armed leading waves. The two-armed trailing waves usually have smalle
r amplifications. The growth rates and amplifications all decrease as
the velocity spreads of the stars and/or gas increase. It is suggested
that the spiral waves can provide an effective viscosity for the gas
causing its accretion.