  We present new types of regularity for nonlinear generalized functions, based
on the notion of regular growth with respect to the regularizing parameter of
Colombeau's simplified model. This generalizes the notion of G^{\infty
}-regularity introduced by M. Oberguggenberger. A key point is that these
regularities can be characterized, for compactly supported generalized
functions, by a property of their Fourier transform. This opens the door to
microanalysis of singularities of generalized functions, with respect to these
regularities. We present a complete study of this topic, including properties
of the Fourier transform (exchange and regularity theorems) and relationship
with classical theory, via suitable results of embeddings.
