  We develop the off-shell nilpotent finite field dependent BRST
transformations and show that for different choices of the finite field
dependent parameter these connect the generating functionals corresponding to
different effective theories. We also construct both on-shell and off-shell
finite field dependent anti-BRST tranformations for Yang Mills theories and
show that these transformations play the similar role in connecting different
generating functionals of different effective theories. Analogous to the finite
field dependent BRST transformations, the non-trivial Jacobians of the path
integral measure which arise due to the finite field dependent anti-BRST
transformations are responsible for the new results. We consider several
explicit examples in each case to demonstrate the results.
