PSPACE is a strict superset of the set of context-sensitive languages.
It turns out that allowing the Turing machine to be nondeterministic does not add any extra power. Because of Savitch's theorem, NPSPACE is equivalent to PSPACE, essentially because a deterministic Turing machine can simulate a nondeterministic Turing machine without needing much more space (even though it may use much more time). Also, the complements of all problems in PSPACE are also in PSPACE, meaning that Co-PSPACE = PSPACE.
Read more about PSPACE: Relation Among Other Classes, Other Characterizations, PSPACE-completeness