  Many barred galaxies, possibly including the Milky Way, have cusps in the
centres. There is a widespread belief, however, that usual bar instability
taking place in bulgeless galaxy models is impossible for the cuspy models,
because of the presence of the inner Lindblad resonance for any pattern speed.
At the same time there are numerical evidences that the bar instability can
form a bar. We analyse this discrepancy, by accurate and diverse N-body
simulations and using the calculation of normal modes. We show that bar
formation in cuspy galaxies can be explained by taking into account the disc
thickness. The exponential growth time is moderate for typical current disc
masses (about 250 Myr), but considerably increases (factor 2 or more) upon
substitution of the live halo and bulge with a rigid halo/bulge potential;
meanwhile pattern speeds remain almost the same. Normal mode analysis with
different disc mass favours a young bar hypothesis, according to which the bar
instability saturated only recently.
