  We prove that closed symplectic four-manifolds do not admit any smooth free
circle actions with contractible orbits, without assuming that the actions
preserve the symplectic forms. In higher dimensions such actions by
symplectomorphisms do exist, and we give explicit examples based on a
construction of Fernandez, Gray and Morgan. We also prove that the only compact
complex surfaces admitting free circle actions with contractible orbits are
primary Hopf surfaces.
