TE guiding structures consisting of an optically linear dielectric film embedded in dissimilar optically nonlinear unbounded media, are investigated for hysteresis properties. It is shown that many important features can be determined without a knowledge of the electric fields in the nonlinear media and that the eigenvalue equation yields a relation between the guided-wave vector and the field amplitude at the boundary. The power in the system is the important physical quantity and is carried by asymmetric modes that, in the linear limit, are neither odd nor even. This paper explores some of the limitations of such asymmetrically loaded linear dielectric films and shows that they can exhibit optical hysteresis.