The N = 2 topological Yang-Mills and holomorphic Yang-Mills theories o
n simply connected compact Kahler surfaces with p(g) greater than or e
qual to 1 are re-examined. The N = 2 symmetry is clarified in terms of
a Dolbeault model of the equivariant cohomology. We realize the non-a
lgebraic part of Donaldson's polynomial invariants as well as the alge
braic part. We calculate Donaldson's polynomials on H-2,H-0(S,Z) + H-0
,H-2,(S,Z).