This article presents a new method of integrating evolution differential equations—the non-linear Galerkin method—that is well adapted to the long-term integration of such equations.While the usual Galerkin method can be interpreted as a projection of the considered equation on a linear space, the methods considered here are related to the projection of the equation on a nonlinear manifold. From the practical point of view some terms have been identified as small, and sometimes.(but not always) disregarded.