We extend the theory of super Harish-Chandra pairs, originally developed by
Kostant and Koszul for smooth Lie supergroups, to algebraic supergroups over a field
of characteristic zero. We also review the corresponding complex analytic theory
and we give a characterization of the action of an algebraic (resp. complex
analytic) super Harish-Chandra pair on a supervariety (resp. complex analytic
supermanifold).