[en] The study presents a numerical fluid-plasma model of diffusion-controlled surface-wave-sustained discharges in helium gas. The self-consistent behaviour of the discharge based on the interrelation between plasma density and Θ, the power absorbed on average by one electron, is described. The nonlinear process of step ionization in the charged particle balance equation is the main factor, which ensures the self-consistency. However, it is shown that in helium discharges, the ionization frequencies enter the dependence of Θ on the plasma density also through the ambipolar-diffusion coefficient. Results at two different values of the gas pressure and of the wave frequency are discussed. The lower value of the gas pressure is chosen according to the condition to have a pure diffusion-controlled regime without interference with a transition to the free-fall regime. The boundary condition for the ion flux at the wall sheath is used for determination of the value of μ, the quantity denoting the degree of the radial plasma-density inhomogeneity which, together with the electron-neutral elastic collision frequency, influences the wave propagation characteristics. The two values of the wave frequency chosen provide descriptions of high-frequency and microwave discharges. The model results in the self-consistent structure of the discharge: interrelated variations along the discharge length of wavenumber, space damping rate, Θ, plasma density and electron temperature. The power necessary for sustaining discharges of a given length is also calculated. Comparisons with argon discharges are shown