Abstract: We consider an eigenvalue problem for Laplace operator in a two-dimensional straight strip. We impose Dirichlet condition everywhere on the boundary except for a segment on the boundary on which we settle Neumann condition. We prove that increase of this segment length gives birth to new eigenvalues emerging from the continuum. We find asymptotic expansions for these new eigenvalues and derive explicit formulae for their leading terms. This is a joint work with P. Exner and R. Gadyl'shin.