[citation needed] In 1983, Douady was appointed to the Centre National de la Recherche Scientifique (CNRS).

[citation needed] Douady worked on the Kolmogorov–Arnold–Moser (KAM) theorem on the existence of invariant tori in Hamiltonian systems.

[4] He contributed to the theory of outer billiards, providing a full proof of a result announced earlier by J. Moser.

[6] In 1999, he established with Jean-Christophe Yoccoz a theory of automorphic measures of circle diffeomorphisms, a basis for differentiating the rotation number function.

He established a generalization of Heath–Jarrow–Morton interest rate model, where the yield curve is represented as a random field.

[8] With Monique Jeanblanc, he created a rating-based credit derivatives model that introduced the notion of "rating surface".

[11] In a book co-authored with Thomas Barrau, he demonstrated that Polymodels are applicable to a wide range of problems in finance, especially the question of forecasting the behavior of equity and fixed income markets.