The properties of strongly optically nonlinear waves guided by Kerr-like dielectric media, in which the refractive index depends upon the intensity of the waves, have attracted a lot of attention over the last few years [1–16]. This area is so important now that a number of very interesting device applications have already been proposed . The recent emphasis on the optical Kerr effect is understandable because it has its origins in the third order terms of an expansion of the electric polarization in powers of the electric field. Such terms reveal that optical signal processing is permitted with the same input and output frequency, for materials with a centre of symmetry. This is essential from a device point of view and considerably simplifies the boundary conditions. If the total power flow down the guide is very weak then the electric field distribution, to a first approximation, is not greatly disturbed. Even in this case, however, there is still a small, first order change in the guided wavenumber that can be exploited as an accumulated phase shift picked up from a specific structure, such as a grating. This kind of distributed coupling can be analysed theoretically with the usual coupled mode theory . The nonlinearity discussed here is not weak and the guiding situations discussed will involve field distributions that are so strongly distorted that self-focussing may occur. This will, basically, occur when the refractive index change due to the nonlinearity becomes the same order of magnitude as the difference between the linear parts of the refractive indices of the two adjacent media. It is also being appreciated now, that a given material in an experiment may not exhibit a Kerr-type nonlinearity [11,12]. As will be indicated below, this can be introduced into the theory by modelling saturation effects and other power-law non-Kerr behaviour in a fairly straightforward manner.