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The results of part I (hep-ph/9612284) are used to obtain full asymptoticexpansions of Feynman diagrams renormalized within the MS-scheme in the regimeswhen some of the masses and external momenta are large with respect to theothers. The large momenta are Euclidean, and the expanded diagrams are regardedas distributions with respect to them. The small masses may be equal to zero.The asymptotic operation for integrals is defined and a simple combinatorialtechniques is developed to study its exponentiation. The asymptotic operationis used to obtain the corresponding expansions of arbitrary Green functions.Such expansions generalize and improve upon the well-known short-distanceoperator-product expansions, the decoupling theorem etc.; e.g. the low-energyeffective Lagrangians are obtained to all orders of the inverse heavy mass. Theobtained expansions possess the property of perfect factorization of large andsmall parameters, which is essential for meaningful applications tophenomenology. As an auxiliary tool, the inversion of the R-operation isconstructed. The results are valid for arbitrary QFT models.Comment: one .sty + one .tex (LaTeX 2.09) + one .ps (GSview) = 46 pp. Many  fewer misprints than the journal versio

EUCLIDEAN ASYMPTOTIC EXPANSIONS OF GREEN FUNCTIONS OF QUANTUM FIELDS (II) COMBINATORICS OF THE AS OPERATION