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A model of atmospheric-pressure air discharges sustained by electromagnetic surface waves is developed that accounts for deviation of plasma state from the local thermodynamic equilibrium. Calculated distributions of plasma parameters along the discharge axis are presented for a wide wave-frequency range (from RF to microwaves). Values of the discharge length are given, depending on the wave frequency, the tube radius and the power input. It is shown that effects of ionization nonequilibrium become important at low values of the wave frequency and the discharge power. Parameters of microwave discharges in N2-O2 mixtures, at small content of oxygen, are calculated and compared with available experimental data.