This paper fills a gap in the theory of equilibrium and stability of s
tellar disks: it analyzes models with an arbitrary degree of radial el
ongation of stellar orbits, whereas all previous investigations consid
ered only nearly circular orbits. We study a series of distribution fu
nctions that are disk analogs of generalized polytropic models of sphe
rical systems. The latter have been recently explored in detail and pr
oved extremely fruitful. We hope that disk polytropes will be equally
useful primarily for understanding the formation of bars in SB galaxie
s and related structures (rings, spirals, etc.). Using N-body simulati
ons we derived a crude estimate of the stability limit. It corresponds
to a disk in which the radial part of kinetic energy is nearly twice
as much as the transversal part. This instability leads to the formati
on of a well-defined bar that slowly rotates with a velocity approxima
tely equal to the precession velocity of a typical stellar orbit.