  A substantial fraction of disk galaxies is double-barred. We analyze the
dynamical stability of such nested bar systems by means of Liapunov
exponents,by fixing a generic model and varying the inner (secondary) bar mass.
We show that there exists a critical mass below which the secondary bar cannot
sustain its own orbital structure, and above which it progressively destroys
the outer (primary) bar-supporting orbits. In this critical state, a large
fraction of the trajectories (regular and chaotic) are aligned with either bar,
suggesting the plausibility of long-lived dynamical states when
secondary-to-primary bar mass ratio is of the order of a few percent.
Qualitatively similar results are obtained by varying the size of the secondary
bar, within certain limits, while keeping its mass constant. In both cases, an
important role appears to be played by chaotic trajectories which are trapped
around (especially) the primary bar for long periods of time.
