The generalized Schrödinger equation d 2 /dx 2 ϩF(k)ϭ͓ikP(x)ϩQ(x)͔ is considered, where P and Q are integrable potentials with finite first moments and F satisfies certain conditions. The behavior of the scattering coefficients near zeros of F is analyzed. It is shown that in the so-called exceptional case, the values of the scattering coefficients at a zero of F may be affected by P(x). The location of the k-values in the complex plane where the exceptional case can occur is studied. Some examples are provided to illustrate the theory.