Theory of the figures of equilibrium was developed actively during XIX century when causes were discovered making the form of observable massive celestial bodies (the Sun, planets, moons) almost ellipsoidal. The existence of exactly ellipsoidal figures was established. The gravitational potential of such figures can be presented by the Laplace series. Its coefficients (harmonic coefficients, or Stokes constants In) are determined via one of two ways, first, by a definite integral operator if density distribution inside the body is known, second, by a certain transformation of the outer gravitational potential if it is known. In the present paper asymptotics of In is found using the first approach for an ellipsoid if its equidensites (surfaces of equal density) are ellipsoids of revolution. It is supposed that equidensites’ oblateness increases from the centre to the periphery. It turned up that asymptotics depend on the mean density, density on the surface of the boundary ellipsoid, and its oblateness only. Coefficients In and their asymptotics are found using the second approach for a level ellipsoid. Both asymptotics coincide for Maclaurin ellipsoids only. Hence, if the level ellipsoid is not a Maclaurin one then its equidensites cannot be ellipsoids.