  Dynamical models of prototype gravastars were constructed in order to study
their stability. The models are the Visser-Wiltshire three-layer gravastars, in
which an infinitely thin spherical shell of stiff fluid divides the whole
spacetime into two regions, where the internal region is de Sitter, and the
external is Schwarzschild. It is found that in some cases the models represent
the "bounded excursion" stable gravastars, in which the thin shell is
oscillating between two finite radii, while in other cases they collapse until
the formation of black holes. In the phase space, the region for the ``bounded
excursion" gravastars is very small in comparison to that of black holes, but
not empty. Therefore, although the existence of gravastars cannot be excluded
from such dynamical models, our results do indicate that, even if gravastars
indeed exist, they do not exclude the existence of black holes.
