  We use a Becchi-Rouet-Stora-Tyutin (BRST) superspace approach to formulate
off-shell nilpotent BRST and anti-BRST transformations in four dimensional N=1
supersymmetric Yang-Mills theory. The method is based on the possibility of
introducing auxiliary fields through the supersymmetric transformations of the
superpartener of the gauge potential associated to a supersymmetric Yang-Mills
connection. These fields are required to achieve the off-shell nilpotency of
the BRST and anti-BRST operators. We also show how this off-shell structure is
used to build the BRST and anti-BRST invariant gauge-fixing quantum action.
