The physical effect known as stepwise precession is a surprising fact that takes place in the movement of an elastic pendulum. When this pendulum is initially set near the downward equilibrium vertical configuration, with the length of the spring stretched by the gravity force, there is a chance to move in such a way that the springing vibrational mode of movement and the rotational "swing" mode interchange periodically their respective energies, with a periodic change of the swing plane and stepwise precession. We simulate here numerically the same dynamical behaviour for the natural extension of a double elastic-spherical pendulum.