Jona-Lasinio G., Seneor R. Study of stochastic differential equations by constructive methods. I. (191K, uuencoded, gzip-compressed Postscript file) ABSTRACT. In this work we give an algorithm to express as a convergent series the stationary averages for a class of gradient perturbations of a non symmetric (non gradient) Orstein-Uhlenbeck process. The method relies on a cluster expansion in time of the Girsanov-Cameron-Martin formula for the density of the perturbed measure with respect to the Orstein-Uhlenbeck measure. In the second paper of this series, the approach is extended to more general perturbations. (195K, Latex)