  We introduce quasi-Hopf $*$-algebras i.e. quasi-Hopf algebras equipped with a
conjugation (star) operation. The definition of quasi-Hopf $*$-algebras
proposed ensures that the class of quasi-Hopf $*$-algebras is closed under
twisting and additionally, that any Hopf $*$-algebra becomes a quasi-Hopf
$*$-algebra via twisting. The basic properties of these algebras are developed.
The relationship between the antipode and star structure is investigated.
Quasi-triangular quasi-Hopf $*$-algebras are introduced and studied.
