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Let f:Rⁿ, 0 → R^p a C^∞ map-germ and let us consider the local algebra of order k, Q_Γ (f) = E_n / f * M_p + M^k+1_n associated with germ f, where E_n is the ring of germs g : Rⁿ , 0 → R and M_n, is the maximal ideal of germs g : Rⁿ, 0 → R, 0. The Classification ot Stable Germs Theorem through the local algebras is classic: "If f and g are stable, them f and g are A-equivalent if, and only if, the associated algebras are isomorphic"; see, J. Mather [10]. In [3], J.P. Dufour has introduced the notion of stabliitv for couples of germs (f₁, f₂) : Rⁿ, 0 → R^p x R^q, 0 and has studied the problem of deformations and classification in particular cases, with his own techniques of dlfficult generalization. The objective of this work is the classification of couples of bi-stable germs, by means of the local algebras associated with (f₁, f₂) and and their components, To reach this objective we introduced the notion of cohorent inomorphiom as follows: Let Φ₁ : E_n / I_f1 + M^k+1_n → E_n / I_g1 + M^k+1_n and Φ₂ : E_n / I_f2 + M^k+1_n → E_n / I_g2 + M^k+1_n, be isomorphisms between two algebras associated with the components of the couples (f₁, f₂, (g₁, g₂) : Rⁿ, 0 → R^p x R^q, 0. Let us suppose that there are isomorphism θ_{1 and θ2 of En, for which we have Φ1 (α + If1 + M^k+1n) = θ1 (α) + Ig1 + M^k+1n and Φ2 (α + If2 + M^k+1n) = Φ2 (α) + I,sub>g2} + M^k+1_n. We say that isomorphism Φ₁ and Φ₂ are induced by Phi;₁ and Phi;₂, respectivaly. (We observe that whenever f K~g then the algebra Q_k(f) and Q_k(g) are isomorphic vie an induced isomorphical). We say, then, that the isomorphism Φ₁ and Φ₂ are coherent when they are indiced by the same isomorphism θ : E_n → E_n. (We prove that whenever (f₁, f₂) Bi-K ~(g₁, g₂ then the algebras Q_k(f₁) and Q_k(g₁, Q_k (f₂) and Q_k(g₂ are isomorphic according to coehent isomorphism, i.e., isomorhism induced by the only ring-isumorphisms θ : E_n → E_n (see chapter IV, 3). Thus the principal theorem can be enunciated: "If bthe couple of germs (F₁, f₂) and (g₁, g₂) are bi-stable, then they are bi-A-equivalent if, and only if, the associated algebras are isomorphic through coherent isomorphisms".