  A new approach to the algebra G_{\tau} of temperate nonlinear generalized
functions is proposed, in which G_{\tau} is based on the space O_{M} endowed
with is natural topology in contrary to previous constructions. Thus, this
construction fits perfectly in the general scheme of construction of Colombeau
type algebras and reveals better properties of G_{\tau}. This is illustrated by
the natural introduction of a regularity theory in G_{\tau}, of the Fourier
transform, with the definition of G_{O_{C prime}}, the space of rapidly
generalized distributions which is the Fourier image of G_{\tau}.
