The conditions of stability of the constant libration solutions of the general three-bodies problem obtained by E. Routh through investigation of the linearized perturbed motion equations are analised. To the values of the masses of the three bodies which satisfy boundary conditions of the region of stability the locus of all corresponding centers of masses is laid down in accordance with. It occurs that this locus is a circle, its centre coinciding with the geometric centre of the trianglem ₁, m₂, m₃ and its radius being a function of exponent in the law of attraction of the bodies. The motion may be stable only if the centre of masses of the bodies lies outside the circle mentioned above. In the case of the Newtonian law of attraction the radius of this circle equals 0,943 |r_max| where |r_max| is a distance of the vertex from the centre of the trianglem ₁, m₂, m₃. Thus stability is possible (if it is generally possible) inside a very small region in this case.