  Over an arbitrary field of characteristic $\ne 2$, we define the notion of
Harish-Chandra pairs, and prove that the category of those pairs is
anti-equivalent to the category of algebraic affine supergroup schemes. The
result is applied to characterize some classes of affine supergroup schemes
such as those which are (a) simply connected, (b) unipotent or (c) linearly
reductive in positive characteristic.
