  The monopole equations in the dual abelian theory of the N=2 gauge-theory,
recently proposed by Witten as a new tool to study topological invariants, are
shown to be the simplest elements in a class of instanton equations that follow
from the improved topological twist mechanism introduced by the authors in
previous papers. When applied to the N=2 sigma-model, this twisting procedure
suggested the introduction of the so-called hyperinstantons, or triholomorphic
maps. When gauging the sigma-model by coupling it to the vector multiplet of a
gauge group G, one gets gauged hyperinstantons that reduce to the
Seiberg-Witten equations in the flat case and G=U(1). The deformation of the
self-duality condition on the gauge-field strength due to the
monopole-hyperinstanton is very similar to the deformation of the self-duality
condition on the Riemann curvature previously observed by the authors when the
hyperinstantons are coupled to topological gravity. In this paper the general
form of the hyperinstantonic equations coupled to both gravity and gauge
multiplets is presented.
