The influence of longitudinal manetic field (MF) on a position of polarization planes (PPs) of the main modes (λ = 0.63 µm) in dependency on the generation frequency and off-axis mode presence was investigated in this work. It was shown that mode PPs are strictly orthogonal only in their symmetrical position in the amplification contour. In other spectral ranges PP position depends on the value of cavity anisotropy and local MF. Local MF action is equivalent to that of homogeneous MF. Characteristics of axis modes (intensity, PP position, optical frequency and especially an inter-mode beating frequency) are destabilized by modes of higher orders, dynamics of which possesses a random character. Nonlinear interaction between modes and a strong dependency of their characteristics on a local MF make stabilization system reliable operation impossible, if these systems are based only on internal properties of laser emission. The high sensitivity of the polarization state to the local MF can be used for broad-band polarizational modulation of laser emission.