Studies of multiphoton-induced X-ray generation in Kr and Xe clusters give direct information concerning (1) the atom-specific energy transfer rate, (2) the dependence of the X-ray yield on the strength of the intra-cluster inelastic electron scattering cross section, and (3) the threshold intensity for X-ray generation. Measurements of these three classes of observables with subpicosecond ( approximately 300 fs) ultraviolet (248 nm) radiation at a maximum intensity of approximately 10¹⁹ W cm^-2 all indicate that the non-linear coupling to the cluster has an anomalous strength with respect to that derivable from conventional single-particle interactions. Five cases have been examined (Kr(M), Kr(L), Xe(N), Xe(M) and Xe(L)), spectrally spanning the range from approximately 80 eV to approximately 5 keV. In order to reconcile theoretical estimates with these experimental findings, three generalizations of the original formulation of the interaction were necessary. The most important involves an enhancement in the coupling arising from the coherent motion of the (Z) field-ionized electrons induced by the external driving field. The coherently energized electrons act like a quasi-particle possessing a charge Ze and a mass Zm, thereby presenting a sharply augmented coupling resembling that associated with energetic ion-atom collisions. The second involves the process of multiple electron ejection from an inner-shell, a mechanism that was found imperative to interpret the high level of ionization observed in the Xe M-shell. The third modification concerns multiple transits of the driven electrons in the cluster. The inclusion of these considerations consistently brings the theoretical analysis into agreement with the three measured properties. These results also indicate that energy deposition rates exceeding approximately 1 W/atom are feasible in appropriately designed molecules incorporating heavy atoms. The limiting magnitude of the excitation energy Delta E_max characteristic of the coherent coupling is estimated to be in the range Zamc²<or= Delta E_max<or=Z²amc², a bound that can considerably exceed the K-shell binding energy of the heaviest atoms.