Stability with respect to tilting the axis of rotation is studied for various modes of the rotational motion of a nonspherical satellite in an elliptical orbit. The axis of the rotational motion, whose stability is investigated, is assumed to coincide with the axis of the largest moment of inertia and to be orthogonal to the orbital plane. For a representative set of initial data, the distributions of the values of the maximum characteristic Lyapunov exponent are calculated and analyzed. On this basis, for Hyperion, Phobos, Deimos and Amalthea, the trajectories of planar rotational motion (with the axis of rotation orthogonal to the orbital plane of the satellite) are classified into those that are stable and those that are unstable, with respect to tilting the axis of rotation, regardless of the type of the planar trajectory (periodic, quasi-periodic, or chaotic), whose stability is investigated. The basic spin-orbital states, in which the referenced satellites can occur during the course of their dynamical evolution at eccentricities close to the contemporary values, are found.