  In this paper we compute the first and second variation of the normalized
Einstein-Hilbert functional on CR manifolds. We characterize critical points as
pseudo-Einstein structures. We then turn to the second variation on standard
spheres. While the situation is quite similar to the Riemannian case in
dimension greater or equal to five, in three dimension we observe a crucial
difference, which mainly depends on the embeddable character of the perturbed
CR structure.
