  The extended BRST cohomology of N=2 super Yang-Mills theory is discussed in
the framework of Algebraic Renormalization. In particular, N=2 supersymmetric
descent equations are derived from the cohomological analysis of linearized
Slavnov-Taylor operator $\B$. It is then shown that both off- and on-shell N=2
super Yang-Mills actions are related to a lower-dimensional gauge invariant
field polynomial $Tr\f^2$ by solving these descent equations. Moreover, it is
found that these off- and on-shell solutions differ only by a $\B-$exact term,
which can be interprated as a consequence of the fact that the cohomology of
both cases are the same.
