  High-resolution observations of the inner regions of barred disk galaxies
have revealed many asymmetrical, small-scale central features, some of which
are best described as secondary bars. Because orbital time-scales in the galaxy
center are short, secondary bars are likely to be dynamically decoupled from
the main kiloparsec-scale bars. Here, we show that regular orbits exist in such
doubly-barred potentials and that they can support the bars in their motion. We
find orbits in which particles remain on loops: closed curves which return to
their original positions after two bars have come back to the same relative
orientation. Stars trapped around stable loops could form the building blocks
for a long-lived, doubly-barred galaxy. Using the loop representation, we can
find which orbits support the bars in their motion, and what are the
constraints on the sizes and shapes of self-consistent double bars. In
particular, it appears that a long-lived secondary bar may exist only when an
Inner Lindblad Resonance is present in the primary bar, and that it would not
extend beyond this resonance.
