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We have previously introduced the parameter `alpha' as an indicator ofstability to m=2 nonaxisymmetric modes in rotating, self-gravitating,axisymmetric, gaseous and stellar systems. This parameter can be written as afunction of the total rotational kinetic energy, the total gravitationalpotential energy, and as a function of the topology/connectedness and thegeometric shape of a system. Here we extend the stability criterion tononaxisymmetric equilibrium systems, such as ellipsoids and elliptical disksand cylinders. We test the validity of this extension by consideringpredictions for previously published, gaseous and stellar, nonaxisymmetricmodels. The above formulation and critical values account accurately for thestability properties of m=2 modes in gaseous Riemann S-type ellipsoids(including the Jacobi and Dedekind ellipsoids) and elliptical Riemann disks aswell as in stellar elliptical Freeman disks and cylinders: all these systemsare dynamically stable except for the stellar elliptical Freeman disks thatexhibit a relatively small region of m=2 dynamical instability.Comment: 17 pages, postscript, compressed, uuencoded. 10 figures available by  anonymous ftp from ftp://asta.pa.uky.edu/shlosman/bar2/ (mget *.ps.Z). To  appear in Ap.J

A new criterion for bar-forming instability in rapidly rotating gaseous and stellar systems. 2: Nonaxisymmetric form