In this work we obtain two results related to multi-linear p-compact operators in Banach spaces. The first result establishes that an operator Φ ε ℒ(E1,...,En,F) is p-compact (1 ≤ p ≤ ∞) related to (q1,...qn) if and only if there exist the operators ψ ε ℒ(E1,...,En,lp) and A ε ℒ(lp, F) such that Φ = A o ψ, where A, ψ are compact. One has N(∞,p;q1,...qn) (Φ) = in f ∥ A ∥ ∥ ψ ∥, where the infimum is taken over all possible factorizations. The second result is concerned with any multi-linear operator of finite type ψ ε ℒ (E1,...,En, L p(Ω, μ )) and establishes the following result: N (∞p;q1,...qn) (Φ) = Nf, (∞,p;q1,...qn) (ψ) = ∥ψ∥. © 2009 Academic Publications.