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

How can double-barred galaxies be long-lived?