On the basis of Jones' vectors and matrices formalism the equations of
motion have been derived for two-frequency Fabry-Perot gas laser with
a weakly anisotropic cavity when an active medium is placed in an axi
al magnetic field. The case of linear phase anisotropy is considered i
n detail. In lasers, operating at j --> j + 1 transitions in the absen
ce of any external effects, the possibility of existence of polarizati
on instability is shown. The influence of frequency detuning from the
gain profile center on the operation of two-frequency laser has been c
onsidered. Polarization multistability has been predicted. The polariz
ation dynamics of a laser in a longitudinal magnetic field has been in
vestigated. The results of the theory are in agreement with the known
experimental data.