[en] This work reports on measurements and calculations (coupled mode equations) on the conversion of circular elecric TEsub(0n) gyrotron mode compositions (TE₀₁ to TE₀₄) at 28 and 70 GHz to the linearly polarized TE₁₁ mode by means of a mode converter system using periodic waveguide wall perturbations. Mode transducers with axisymmetric radius perturbations transform the TEsub(0n) gyrotron mode mixture to the more convenient TE₀₁ mode for long-distance transmission through overmoded waveguides. Proper matching of the phase differences between the TEsub(0n) modes and of lengths and perturbation amplitudes of the several converter sections is required. A mode converter with constant diameter and periodically perturbed curvature transfers the unpolarized TE₀₁ mode into the TE₁₁ mode which produces an almost linearly polarized millimeter-wave beam needed for efficient electron cyclotron heating (ECRH) of plasmas in thermonuclear fusion devices. The experimentally determined TEsub(0n)-to-TE₀₁ conversion efficiency is (98+-1)% at 28 and 70 GHz (99% predicted) while the TE₀₁-to-TE₁₁ converter has a (96+-2)% conversion efficiency at 28 GHz (95% predicted) and (94+-2)% at 70 GHz (93% predicted); ohmic losses are included. (orig./AH)