Stellar disks having two equal populations of stars rotating in opposi
te directions are subject to several distinct instabilities. Here we f
ocus on the six lowest-order modes: three within the disk plane and th
ree bending modes. The form and vigor of the principal instabilities i
n any individual model vary with the balance between radial and azimut
hal pressure and with disk thickness: thin radially hot models have di
sruptive axisymmetric bending instabilities (bell modes), while an in-
plane lopsided instability is the most disruptive for cool models. All
instabilities are weakened, but most rather slowly, by increasing dis
k thickness. The nonlinear evolution of the more unstable models takes
an exotic variety of forms including lopsided and warped disks, perma
nent asymmetries about the initial plane, and pairs of counterrotating
bars. Some of the radially hotter models acquire a thick subcomponent
in the disk center resembling a bulge in appearance. Remarkably, howe
ver, the instabilities in a model having intermediate radial pressure
cause rather mild changes and lead to an apparently stable, moderately
thin, and almost axisymmetric disk. This model indicates that the SO
galaxy NGC 4550, which has recently been discovered to possess two cou
nterrotating disks, does not require large quantities of unseen mass t
o stablize it. This final state is also an unusual counterexample to t
he claim that instabilities should always thicken any nonrotating stel
lar system flatter than E7.