  We show that for N = 1 supersymmetric Yang-Mills theory it is possible to
build an off-shell nilpotent BRST and anti-BRST algebra in terms of a BRST
superspace formalism. This is based on the introduction of the basic fields of
the quantized theory together with an auxiliary real field via the lowest
components of the superfield components of a superYang-Mills connection. Here,
the associated supercurvature is constrained by horizontality conditions as in
ordinary Yang-Mills theory. We also show how the off-shell BRST-invariant
quantum action can be constructed starting from a gauge-fixed superaction.
