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Abstract. The Euclidean massive Gross-Neveu model in two dimensions is just renormalizable and asymptotically free. Thanks to the Pauli principle, bare perturbation theory with an ultra-violet cut-off (and the correct ansatz for the bare mass) is convergent in a disk, whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant. Therefore, the theory can be fully constructed in a perturbative way. It satisfies the O.S. axioms and is the Borel sum of the renormalized perturbation expansion of the model

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Let G be a Euclidean Feynman graph containing L(G) lines. We prove that if G has massive propagators and does not contain any divergent subgraphs its value is bounded by K L(G \ We also prove the infrared analogue of this bound.

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