Wave damping near the electron gyrofrequency in a Tokamak plasma with the energetic tail generated by the electric field is investigated. The electron tail is computed by a Fokker-Planck initial value code as a function of the relevant parameter E/sub ////Ec=E/sub ///Te/(2 pi nee3 Lambda ). It is shown that strong damping of the e-mode occurs for oblique propagation. The results are of relevance for studies of ECRH in present-day Tokamaks and in future reactors where a mildly relativistic electron tail is naturally present for large Te. Special emphasis is therefore given to wave absorption for frequencies of significantly below the central electron gyrofrequency, and to the associated r.f.-driven current.