  For the closed string carrying 2 or 3 point-like masses the stability problem
for central and linear rotational states is considered. This problem is
important for applications of these model to describing baryons, glueballs or
other exotic hadrons. The linear rotational state correspond to an uniform
rotation of the system with rectilinear string segments, connecting massive
points. The state is named ``central'' one, if there is a massive point at the
rotational center. It is shown that the linear rotational states with 2 massive
points are stable with respect to small disturbances. But the central
rotational states with 3 masses are not stable, if the central mass it less
than energy of the string with other massive points. This effect may change
properties of excited hadron states, in particular, increase their width.
