  We consider the magnetic Schrodinger operator in a two-dimensional strip. On
the boundary of the strip the Dirichlet boundary condition is imposed except
for a fixed segment (window), where it switches to magnetic Neumann boundary
condition (see Section 2, Eq. (2.2) for the definition of this boundary
condition}. We deal with a smooth compactly supported field as well as with the
Aharonov-Bohm field. We give an estimate on the maximal length of the window,
for which the discrete spectrum of the considered operator will be empty. In
the case of a compactly supported field we also give a sufficient condition for
the presence of eigenvalues below the essential spectrum.
