The reaction/adsorption of multiple H-2 molecules on Pd-n clusters with n=3 and 4 were studied using the density functional theory. It has been shown that the activation of the first H-2 molecule by Pd-3 and Pd-4 takes place without or with a small energetic barrier (based on DeltaH (298.15 K)) and leads to the formation of Pd-3(H)(2) and Pd-4(H)(2) complexes, respectively, where the H-H bond is broken. For the Pd-4(H)(2) complex, various isomeric structures were found in the singlet and triplet states, among which the singlet Pd4_l_c_(e,e'), with the two H ligands bridging the Pd-Pd edges not sharing the Pd atom, is found to be the most favorable. unlike the first H2 addition reaction, dissociative adsorption of the second H2 molecule, reactions Pd-3(H)(2) + H-2 -> Pd-3(H)(4) and Pd-4(H)(2) + H-2 -> Pd-4(K)(4), appeared to be thermodynamically and kinetically unfavorable. Instead, molecular adsorption of additional mH(2) molecules onto the "naked" Pd centers of the Pdl(H)(2) and Pd-4(H)(2) complexes was shown to be feasible, which is in good agreement with the experimental Pd-n + D-2 saturation studies. The thermodynamic stabilities of the resulting Pd-3(H)(2)(H-2)(m) (m = 1-3) and Pd-4(H)(2)(H-2)(m) (m = 1-4) species were discussed in terms of the DeltaH and ac values estimated at T = 298.15 and 70K.