The origin of the nonlinearity of plasma permittivity in high-frequenc
y discharges maintained by ionizing surface waves is studied. It is sh
own that in a diffusion controlled regime the plasma density at the di
scharge axis is determined nonlocally in terms of the electric field i
ntensity by accounting for the small nonlinear effect of recombination
, along with diffusion in the particle balance equation. The axial sel
fconsistent distribution of the surface wave field intensity and of th
e plasma density of discharges are obtained. The transition to a 'pure
' diffusion and a 'pure' recombination regime is considered. A brief d
iscussion is included regarding the case of a nonlinearity due to a we
ak dependence of the ionization frequency on the plasma density (e.g.
due to stepwise processes).