Termes seculaires dans la theorie des perturbations

The convergence property is examined for the series which appear in the theory of the planetary motions. With another point of view, we obtain a result different from that already given by Gyldén: The almost divergency in the meaning of category is concluded when the ratio of the mean motions is irrational using as Gyldén the continuous fractions. The author explains the reason why the series are always useful in practical applications: Because the long evolution of the system of interest under the influence of the small irreversible effects has led to many resonances or quasi-resonances, i.e. conditions favorable to a good convergence of suitable series.