  I decompose the unstable growing modes of stellar disks to their Fourier
components and present the physical mechanism of instabilities in the context
of resonances. When the equilibrium distribution function is a non-uniform
function of the orbital angular momentum, the capture of stars into the
corotation resonance imbalances the disk angular momentum and triggers growing
bar and spiral modes. The stellar disk can then recover its angular momentum
balance through the response of non-resonant stars. I carry out a complete
analysis of orbital structure corresponding to each Fourier component in the
radial angle, and present a mathematical condition for the occurrence of van
Kampen modes, which constitute a continuous family. I discuss on the
discreteness and allowable pattern speeds of unstable modes and argue that the
mode growth is saturated due to the resonance overlapping mechanism. An
individually growing mode can also be suppressed if the corotation and inner
Lindblad resonances coexist and compete to capture a group of stars. Based on
this mechanism, I show that self-consistent scale-free disks with a sufficient
distribution of non-circular orbits should be stable under perturbations of
angular wavenumber $m>1$. I also derive a criterion for the stability of
stellar disks against non-axisymmetric excitations.
