  The relativistic string with massive ends (the meson model) and four various
string baryon models: q-qq, q-q-q, Y and $\Delta$ are considered. In
particular, the rotational motions for all these systems are applied to
describing the leading Regge trajectories, and also the classical dynamics
beyond the usual rectilinear string rotations is studied. For the string meson
model the two types of quasirotational motions (disturbances of the planar
uniform rotations) are obtained. They are oscillatory motions in the form of
stationary waves in the rotational plane and in the orthogonal direction. The
analysis of the stability problem for the rotational motions for all mentioned
string configurations shows that these motions for the Y and q-q-q models are
unstable on the classical level.
