[en] The hydrogen--deuterium exchange reaction was studied by molecular beam scattering on low and high Miller index crystal faces of platinum in the surface temperature range of 300--1300degreeK. Under the condition of the experiments which put strict limitation on the residence time of the detected molecules, the reaction product, HD, was readily detectable from the high Miller index, stepped surfaces (integrated reaction probability, defined as total desorbed HD flux divided by D₂ flux, is approx.10/sup -1/) while HD formation was below the limit of detectability on the Pt(111) low Miller index surface (reaction probability <10/sup -5/). Atomic steps at the platinum surface must play a controlling role in dissociating the diatomic molecules. The exchange reaction is first-order in D₂ beam pressure and half-order in H₂ background pressure. The absence of beam kinetic energy dependence of the rate indicates that the molecular adsorption does not require activation energy. The surface is able to store a sufficiently large concentration of atoms which react with the molecules by a two-branch mechanism. The rate constants for this two-branch mechanism were determined under conditions of constant H atom coverage, reducing the bimolecular reaction to a pseudo-first-order reaction. At lower temperatures (<600degreeK) the rate constant for the exchange is k₁ = (2plus-or-minus1) times10⁵ exp(-4.5plus-or-minus0.5 kcal/RT) sec/sup -1/. The rate determining step appears to be the diffusion of the D₂ molecule on the surface to a step site where HD is formed via a three-center (atom--molecule) reaction, or via a two-center (atom--atom) reaction subsequent to D₂ dissociation at the step. At higher temperatures (>600degreeK) the reaction between an adsorbed H atom and an incident D₂ gas molecule competes with the low temperature branch. The rate constant for this branch is k₂ = (1plus-or-minus2) times10² exp(-0.6plus-or-minus0.3 kcal/RT) sec/sup -1/