The molecular beam method is applied to study the kinetics of H-2 and D-2 adsorption on the W(1 1 0) surface with the substrate temperature T-S similar to 5 K as a function of the molecular flux F. The character of the effect of flux changes on the adsorption kinetics is essentially different in the cases of H-2 and D-2 adsorption. In the H-2 case, the increase of F from 5 x 10(12) to 2 x 10(14) molecules/cm(2)s modifies the coverage dependence of the sticking probability S(theta) both qualitatively and quantitatively, i.e., (i) the initial sticking probability S-0 increases more than by a factor of two; (ii) the saturation coverage theta (S) considerably increases; (iii) the monotonic (for the lowest F) dependence S(theta) transforms into a dependence with a maximum whose height grows as F increases. In the case of D-2 adsorption, the changes of F in approximately the same range produce relatively weak effect on the adsorption kinetics. In particular, both S-0 and theta (S) are changed insignificantly. The increase of S-0 with rising F is assumed to be caused by the interaction of H-2 molecules in the intrinsic precursor state which leads to the nucleation of the 2D condensed phase. The greater F the higher the nucleation probability. The 2D condensation suppresses the themodesorption from the precursor state and thus leads to the increase of S-0. The growth of theta (S) with increasing F is associated with the instability, for T-S similar to 5 K, of the physisorbed H-2 layer whose dynamically equilibrium coverage increases as F rises. The appearance of a maximum in the S(theta) dependence can be explained by greater efficiency of the energy exchange between the incident H-2 molecules and the surface under the formation of a weakly bound molecular adlayer. The revealed distinctions in the character of the molecular flux influence on the kinetics of H-2 and D-2 adsorption for T-S similar to 5 K are associated with differing quantum properties of these molecules, namely, by the deeper position of the zero-point vibrational level for the heavier D-2 molecule. (C) 2001 Elsevier Science B.V. All rights reserved.