A channel-type model for RF and microwave discharges, operating under a local thermodynamic equilibrium (LTE) regime and sustained by travelling waves, is proposed. Such discharges are, as a rule, axially non-uniform. The channel model presented includes this feature. From the analysis that follows, two functions of the value of the heat flux potential at the axis (SA) turn out to be necessary to determine the spatial structure of the discharge. These are L(SA), the power dissipated per unit length of the plasma column, and alpha (SA), the wave attenuation coefficient. From these, the spatial distribution S(r, z) of the heat flux potential can be obtained. Under LTE conditions, this is sufficient to determine the distributions of all plasma parameters of interest. As an example, the spatial structure of a nitrogen discharge sustained by a surface wave is calculated. © 1990 IOP Publishing Ltd.