Аннотация:Abstract—The secular evolution of axially symmetric two-component models of celestial bodies consisting of a rocky core and an icy shell is considered. For the equilibrium of the model, it is necessary that its outer surface and the surface of the density interface are confocal and level oblate spheroids. Quadratic gravitational potentials and equilibrium angular velocities of rotation of both subsystems are found. These angular velocities are not equal, because the core should rotate slightly faster than the mantle. However, in a real celestial body, due to friction between ice and rock, both components should rotate at the same angular velocity.Therefore, surfaces and cannot be level at the same time, and the figure undergoes internal deviationsfrom equilibrium and additional internal stresses. It is shown that under these conditions the secular evolution of the core and mantle starts to take place: the rocky core will decrease its angular velocity and gradually become more spherical. As a result, there will be additional pressure from the core on the ice along the rotation axis. This pressure from the core stretches the icy shell toward the poles, and when (at intervals of billions of years) it reaches a critical value, fractures and faults will appear at the equator of the figure. To illustrate this action, we consider Charon, a large satellite of Pluto, which, according to the NASA New Horizons mission,indeed has a global equatorial rift. The dimensions and shape of the rocky core and icy shell are found: at the average radius of Charon the semiaxes of the core are and the rock and ice comprise approximately and of the total mass of the moon, respectively. This can not only explain the fracture of the icy mantle at Charon’s equator, but also provides strong arguments in favor ofthe hypothesis of the differential structure of this celestial body.