  Double-barred galaxies account for almost one third of all barred galaxies,
suggesting that secondary stellar bars, which are embedded in large-scale
primary bars, are long-lived structures. However, up to now it has been hard to
self-consistently simulate a disc galaxy that sustains two nested stellar bars
for longer than a few rotation periods. N-body/hydrodynamical simulations
including star formation recipes have been performed. Their properties have
been compared with the most recent observational data in order to prove that
they are representative of double-barred galaxies, even SB0. Overlaps in
dynamical resonances and bar modes have been looked for using Fourier
spectrograms. Double-barred galaxies have been successfully simulated with
lifetimes as long as 7 Gyr. The stellar population of the secondary bar is
younger on average than for the primary large-scale bar. An important feature
of these simulations is the absence of any resonance overlap for several Gyr.
In particular, there is no overlap between the primary bar ILR and the
secondary bar corotation. Therefore, mode coupling cannot sustain the secondary
bar mode. Star formation is identified here as possibly being responsible for
bringing energy to the nuclear mode. Star formation is also responsible for
limiting the amount of gas in the central region which prevents the orbits
sustaining the secondary bar from being destroyed. Therefore, the secondary bar
can dissolve but reappear after approx. 1 Gyr. When star formation is switched
off the dynamical perturbation associated with the secondary bar needs several
Gyr to fully vanish. Double-bars can be long-lived in numerical simulations
with a gaseous component, even in the absence of overlap of resonances or mode
coupling, provided that star formation remains active in the central region
where the nuclear bar lies.
