  For the relativistic string with massive ends, the three-string baryon model
and other string models of the baryon the small disturbances of well known
rotational motions are considered. For the string meson model the two types of
these disturbances (quasirotational motions) are obtained. They are oscillatory
motions in the form of stationary waves in the rotational plane and in the
orthogonal direction. These solutions may be used for describing more wide
spectrum of hadron excitations and for the quantization of this nonlinear
system. For three-string baryon model or Y configuration these quasirotational
motions are more complicated and contain the branch with growing amplitudes.
This consideration proves that for the three-string model with both massless
and massive ends the rotational motions are unstable on the classical level.
