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We study the secular evolution of several exoplanetary systems by extendingthe Laplace-Lagrange theory to order two in the masses. Using an expansion ofthe Hamiltonian in the Poincar\'e canonical variables, we determine thefundamental frequencies of the motion and compute analytically the long-termevolution of the keplerian elements. Our study clearly shows that, for systemsclose to a mean-motion resonance, the second order approximation describestheir secular evolution more accurately than the usually adopted first orderone. Moreover, this approach takes into account the influence of the meananomalies on the secular dynamics. Finally, we set up a simple criterion thatis useful to discriminate between three different categories of planetarysystems: (i) {\it secular} systems (HD 11964, HD 74156, HD 134987, HD 163607,HD 12661 and HD 147018); (ii) systems {\it near a mean-motion resonance} (HD11506, HD 177830, HD 9446, HD 169830 and $\upsilon$ Andromedae); (iii) systems{\it really close to} or {\it in a mean-motion resonance} (HD 108874, HD 128311and HD 183263).

On the extension of the Laplace-Lagrange secular theory to order two in the masses for extrasolar systems