  We consider the spectral problems for the Sturm-Liouville operator generated
by the Dirichlet, Neumann, Dirichlet-Neumann and Neumann-Dirichlet conditions.
The necessary and sufficient condition for the coincidence of the spectrum of
the Dirichlet-Neumann and Neumann-Dirichlet problems is proved. Also the
necessary and sufficient condition for the coincidence of the spectrum, except
zero, of the Dirichlet and Neumann problems is proved. An application to
periodic and anti-periodic problems is given.
