In a weakly ionized medium, there is diffusive transport of magnetic field relative to the neutral gas. The effective diffusion coefficient is quadratic in the magnetic field strength so that the diffusion is nonlinear. We have included this nonlinear diffusion in a simple model of an α-ω dynamo in a slab. A rich variety of solutions, including steady states and steady travelling waves, are found. Our results may be relevant to the generation of magnetic fields in galaxies and in accretion disks around young starts.