This paper presents the results of investigations of experimental samples of slightly anisotropic elliptical-core multimode fiber lightguides (EC-MFL) and a method of measuring their polarization parameters. The investigations of the polarization properties of EC-MFL showed an increase in their polarization stability with an artificial introduction of birefringence. It is also shown that in lines with a length of approx. 10 m depolarization does not exceed a few percent if the angular aperture of the radiation source is &le1/4 of the aperture of the EC-MFL. It is established that the investigated lightguides have a birefringence of nx -ny = 1.8 × 105 and 5.1 × 105 for samples with a ratio of 0.89 and 0.71 for the semiaxes of the elliptical core, respectively.