  The quark mass dependence of the energy spectrum in the Nambu--Goto string
with point--like masses (quarks) at its ends is analyzed. To this end,
linearized equations of motion and boundary conditions in this model are
considered. It is shown that for sufficiently large quark masses, the first
excited state in string spectrum may be arbitrary close to the ground state.
Obviously this points to infrared instability in the system under
consideration. Possible modifications of string model which could remove this
drawback are discussed.
