In scientific literature the electromagnetic waves propagation in gyrotropic elliptic waveguides has not been studied enough due to: 1) difficulties of deriving Helmholtz equations for gyrotropic elliptic waveguides in arbitrary magnetization directions, 2) difficulties of solving Helmholtz equations and deriving the dispersion equations, 3) difficulties of solving the dispersion equations themselves. In this work, for the first time, dispersion equations for longitudinally magnetized gyrotropic elliptic waveguides were solved. Basing on the solutions results, the dependencies of the constant propagation: 1) on the strength and direction of the magnetizing field, 2) on the waveguide ellipticity at a constant ferrite magnetization were investigated. Studies have revealed previously unknown features inherent only to the electromagnetic waves in such waveguides propagation and showed that: 1) with the ferrite magnetization increase -3,1 times the polarization plane rotation angle increases by «5,4 times; 2) the gyrotropic elliptic waveguide polarization plane rotation angle is greater than that of a similar round waveguide. The results show the main advantage of gyrotropic elliptic guide systems over circular ones consists in the possibilities of varying both external and geometric parameters of gyrotropic elliptic guide systems and obtaining significant phase raids, which in turn allows developing more efficient phase shifters.