  We consider skew-products on $M\times \mathbb{T}^2$, where $M$ is the
two-sphere or the two-torus, which are partially hyperbolic and semi-conjugate
to an Axiom A diffeomorphism. This class of dynamics includes the open sets of
$\Omega$-non-stable systems introduced by Abraham, Smale and Shub. We present
sufficient conditions, both on the skew-products and the potentials, for the
existence and uniqueness of equilibrium states, and discuss their statistical
stability.
