The behaviour of plane waves propagating through regions of constant magnetic field is considered in non-linear electromagnetism. By seeking to find which nonlinear theories can support a magnetic field perpendicular to the wave’s propagation and the magnetic component of the wave, Born-Infeld solutions are found and narrowed down to the Born-Infeld system by demanding invariance under electric-magnetic duality transformations. A family could not be directly calculated when extending to a field in a general direction, however it was found that a family similar to the previous cases can support the system. Analogous work with constant electric fields was then done, with similar results.