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Rate equations for anisotropic lasers were investigated theoretically. The effect of anisotropy of optical properties, such as emission cross section and resonant absorption loss, on the laser performance was examined quantitively. Conditions for dual-polarization oscillations (DPO), as well as formulas which relate the output power to the pump power and various other laser parameters, were given. Experiments were carried out using Nd-stoichiometric-laser crystals. There was good agreement between theory and experimental results. DPO laser oscillating mode patterns and output waveforms were also presented.