  The closed string carrying $n$ point-like masses is considered as the model
of a baryon ($n=3$), a glueball ($n=2$ or 3) or another exotic hadron. For this
system the rotational states are obtained and classified. They correspond to
exact solutions of dynamical equations, describing an uniform rotation of the
string with massive points. These rotational states result in a set of
quasilinear Regge trajectories with different behavior. The stability problem
for the so called central rotational states (with a mass at the rotational
center) is solved with using the analysis of small disturbances. These states
turned out to be unstable, if the central mass is less than some critical
value.
