  We study Cohen-Macaulay actions, a class of torus actions on manifolds,
possibly without fixed points, which generalizes and has analogous properties
as equivariantly formal actions. Their equivariant cohomology algebras are
computable in the sense that a Chang-Skjelbred Lemma, and its stronger version,
the exactness of an Atiyah-Bredon sequence, hold. The main difference is that
the fixed point set is replaced by the union of lowest dimensional orbits. We
find sufficient conditions for the Cohen-Macaulay property such as the
existence of an invariant Morse-Bott function whose critical set is the union
of lowest dimensional orbits, or open-face-acyclicity of the orbit space.
Specializing to the case of torus manifolds, i.e., 2r-dimensional orientable
compact manifolds acted on by r-dimensional tori, the latter is similar to a
result of Masuda and Panov, and the converse of the result of Bredon that
equivariantly formal torus manifolds are open-face-acyclic.
