  We present a complete classification, at the classical level, of the
observables of topological Yang-Mills theories with an extended shift
supersymmetry of N generators, in any space-time dimension. The observables are
defined as the Yang-Mills BRST cohomology classes of shift supersymmetry
invariants. These cohomology classes turn out to be solutions of an N-extension
of Witten's equivariant cohomology. This work generalizes results known in the
case of shift supersymmetry with a single generator.
