  We consider two-dimensional waveguide with a rectangular obstacle symmetric
about the axis of the waveguie. We study the behaviour of the Neumann
eigenvalues located below the first threshold when the sides of the obstacle
approach the edges of the waveguide. We show that only one of the eigenvalues
converge to the first threshold, and the rate of convergence depends on whether
the length of the obstacle divided by the width of the waveguide is integer or
not.
