  Torsors under affine groups are generalized in the super context by
super-torsors under affine super-groups. We investigate those super-torsors by
using Hopf-algebra language and techniques. It is explicitly shown, under
suitable assumptions, that every super-torsor arises from an ordinary torsor.
Especially, the objects with affinity restriction, or namely, the affine
super-torsors and the affine ordinary torsors are shown to be precisely in
one-to-one correspondence. The results play substantial roles in ongoing
construction of super-symmetric Picard-Vessiot theory.
