  The formation of two stellar bars within a galaxy has proved challenging for
numerical studies. It is yet not clear whether the inner bar is born via a star
formation process promoted by gas inflow along the outer bar, or whether it is
dynamically assembled from instabilities in a small-scale stellar disc.
Observational constraints to these scenarios are scarce. We present a thorough
study of the stellar content of two double-barred galaxies observed by the MUSE
TIMER project, NGC 1291 and NGC 5850, combined with a two-dimensional
multi-component photometric decomposition performed on the 3.6{\mu}m images
from S4G. Our analysis confirms the presence of {\sigma}-hollows appearing in
the stellar velocity dispersion distribution at the ends of the inner bars.
Both galaxies host inner discs matching in size with the inner bars, suggestive
of a dynamical formation for the inner bars from small-scale discs. The
analysis of the star formation histories for the structural components shaping
the galaxies provides constraints on the epoch of dynamical assembly of the
inner bars, which took place >6.5 Gyr ago for NGC 1291 and >4.5 Gyr ago for NGC
5850. This implies that inner bars are long-lived structures.
