  We investigate the notion of real form of complex Lie superalgebras and
supergroups, both in the standard and graded version. Our functorial approach
allows most naturally to go from the superalgebra to the supergroup and
retrieve the real forms as fixed points, as in the ordinary setting. We also
introduce a more general notion of compact real form for Lie superalgebras and
supergroups, and we prove some existence results for Lie superalgebras that are
simple contragredient and their associated connected simply connected
supergroups.
