  In this paper we introduce Hausdorff locally convex algebra topologies on
subalgebras of the whole algebra of nonlinear generalized functions. These
topologies are strong duals of Fr\'echet-Schwartz space topologies and even
strong duals of nuclear Fr\'echet space topologies. In particular any bounded
set is relatively compact and one benefits from all deep properties of
nuclearity. These algebras of generalized functions contain most of the
classical irregular functions and distributions. They are obtained by replacing
the mathematical tool of $\mathcal{C}^\infty$ functions in the original version
of nonlinear generalized functions by the far more evolved tool of holomorphic
functions. This paper continues the nonlinear theory of generalized functions
in which such locally convex topological properties were strongly lacking up to
now.
