We consider arbitrary-dimensional super and anti-super BF systems by u
sing a superspace formalism. After introducing superconnections and th
eir associated supercurvatures in a superspace, we show how to recover
the off-shell nilpotent BRST transformations of the fields present in
the super BF systems. Our formalism permits us also to obtain an anti
-BRST operator, which leads to the construction of the anti-super BF s
ystems. These latter systems are not fundamentally different from the
super BF systems, since there is a complete mirror symmetry between th
em.