The paper studies the influence of non-rigidity in the stabilization torque transfer circuit from the drive to the platform on the stability of a biaxial indicator gyrostabilizer in a gimbal suspension and presents the results of these theoretical studies. A comparative analysis of physical and mathematical models of such a biaxial gyrostabilizer for each of the stabilization axes has been carried out. The main differences in the character of the influence of non-rigidity in the stabilization loop on the stability of the gyrostabilizer for each axis have been determined. Stability studies have been carried out, including a comparison with a uniaxial indicator gyrostabilizer, both with and without non-rigidity in the stabilization loop. The characteristic differences in the influence of non-rigidity on each of the considered gyrostabilizers are shown. On the basis of this research the requirements to parameters of biaxial indicator gyrostabilizers in a gimbal suspension have been determined.