The reactions of small cationic platinum clusters (Pt-2(+)-Pt-7(+)) with molecular hydrogen were investigated, and the structures of the hydride complexes were analyzed using IR spectroscopy. We determined the relative reaction rates for the addition of the first H-2 molecule to the platinum clusters, and we report the hydrogen saturation coverages observed at high H-2 concentration. High H atom per Pt atom ratios were observed, similar to earlier measurements on other group-10 transition metals. The structures of the fully saturated complexes of Pt-2(+)-Pt-5(+) were investigated using a combination of infrared multiple-photon dissociation (IR-MPD) spectroscopy in the frequency range of 550-2050 cm(-1) and density functional theory-based calculations. We found molecularly bound hydrogen alongside bridge and often atop binding of hydrogen atoms for all of the low-energy structures, in contrast to earlier theoretical predictions.