Fonctions généralisées et analyse non standard.

We study some connections between Non-Standard Analysis and algebraical theories of generalized functions. More precisely, we point out the fact that the construction of these algebras can be interpreted in terms of Non Standard asymptotic properties. For example, we show that the construction of the J. F. Colombeau'Algebra is equivalent (in a certain sense) to a monadic property. Conversely, we show that a certain galactic property (being exponentially small with respect to a parameter) leads to a new algebra. [ABSTRACT FROM AUTHOR]