The magnetic configurations of two stellarators, ATF [Fusion Technol.10, 170 (1986)] and TJ‐II [Fusion Technol.13, 315 (1986)], are used as examples to study the influence that a superthermal component in the electron distribution function has upon the electron cyclotron resonance heating absorption process for microwaves propagating in the first and second harmonic of the electron cyclotron frequency. The non‐Maxwellian tail is simulated by adding a drifting Maxwellian to a bulk distribution function and an analytical form of the weakly relativistic dielectric tensor is obtained. The quantitative, and more importantly, the qualitative differences between nonrelativistic and relativistic models are also presented. A numerical analysis shows that an increase of up to 50% in the absorption power with respect to the pure Maxwellian models, can be obtained if sufficient superthermal populations are present in the plasma.