  The stability of a recently proposed general relativistic model of galaxies
is studied in some detail. This model is a general relativistic version of the
well known Miyamoto-Nagai model that represents well a thick galactic disk. The
stability of the disk is investigated under a general first order perturbation
keeping the spacetime metric frozen (no gravitational radiation is taken into
account). We find that the stability is associated with the thickness of the
disk. We have that flat galaxies have more not-stable modes than the thick ones
i.e., flat galaxies have a tendency to form more complex structures like rings,
bars and spiral arms.
