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For M ∈ R-Moit anil τ ∈ M-tors, we define the concept of fully τ-hounded module as a generalization of the concept of fully x-hounded ring. We prove that for a x-noetherian module M with local τM-Gahrie! correspondence, which is a progenerator of σ[M] and with tau; is FIS-invariant, then M is fully x-hounded. Also, we show that if M is τ-noetherian and fully τ-hounded, then M has local τM-Gabriel correspondence. [ABSTRACT FROM AUTHOR]