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Manin's relations characterize period polynomials of a modular form. In thispaper, we propose a finite set of relations checked by bi-period polynomials ofa couple of forms. Then we construct an Eisenstein part of depth 2 whichessentially completed the set of bi-periods polynomials among polynomialscanceled by the relations. By giving a computational description of that part,we prove a result of irrationality of ratio of the periods for some weights.

Relations de Manin d'ordre 2 v\'erifi\'ees par le polyn\^ome des bi-p\'eriodes d'un couple de formes modulaires