We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state p = (g-1)rho where g is a constant. The field equations determine two families of spacetimes which describe homogeneous Kantowski-Sachs universes and inhomogeneous Friedmann universes. The ghost field permits static and cyclic solutions to exist. The stability of the Einstein static and cyclic solutions are studied with a critical point analysis.