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Abstract We consider the Szekeres universe with an inhomogeneous dust fluid and a homogeneous and isotropic ghost matter source with equation of state $$p_{g}=( \gamma -1) \rho _{g},$$ pg=(γ-1)ρg, where $$\gamma $$ γ 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.