The authors consider a motion of a spacecraft with small aerodynamic-mass asymmetries in the rarefied layers of the martian atmosphere at small values of the angle of attack. As is known, that small aerodynamic-mass asymmetries of the spacecraft can lead to loss of stability in the angle of attack, caused by the influence of resonant phenomena. The purpose of this study is to obtain a condition of the stability of the relative motion of an asymmetric spacecraft with respect to the angle of attack in a rarefied atmosphere of Mars. The application of the averaging method makes it possible to obtain the second-approximation equation for the angle of attack which form is close to the linear homogeneous equation. The averaged equation allows us to formulate the required stability condition. The theoretical significance of this study is the condition of the stability of the motion of a spacecraft with respect to the angle of attack as solid body in a rarefied atmosphere. The presented condition of the stability was used at research of the motion of the conical spacecraft with respect to the angle of attack in a rarefied atmosphere of Mars. In this case, the mass-inertial parameters of the spacecraft were similar to those of the descending capsule "Schiaparelli". Of practical interest is the use of the obtained stability condition in the analysis of the relative motion of asymmetric spacecraft in the rarefied layers of the atmosphere of the terrestrial planets.