The energetics of self-diffusion within ordered bilayer assemblies of linear hydrocarbons on Pt(111) (layer-to-layer) ha ve been characterized using isothermal molecular beam-surface scattering in conjunction with temperature programmed desorption (TPD) and reflection-absorption infrared (RAIR) spectroscopies. The bilayers are prepared by layering a perdeuterated n-alkane on top of a perprotio n-alkane (or vice versa). The exchange of molecules between the two layers is weakly activated, less so than is either desorption of the multilayer from the substrate (the monolayer is more strongly bound) or the various phase transitions which lead to the loss of two-dimensional order in a corresponding densely-packed monolayer of the n-alkanes. The exchange process is further characterized by substantial size-asymmetry and isotope substitution effects which result in a preference for the selective retention of the longer and (for identical chain lengths) the protio hydrocarbon at the surface regardless of the initial deposition order. Layer-to-layer exchange occurs by a displacive mechanism which follows simple mass action principles : increasing the coverage of the post-absorbed species increases the extent of exchange. The difference in the activation energy for desorption (from the bilayer) and for exchange is similar to 1.5 kcal/mol for both a C-8 and C-10 perdeuterated n-alkane displacing an adsorbed (protio) chain of equal length. Thus, although the activation energy for self-diffusion increases with chain length, it is always less than the activation energy for sublimation by a constant amount. The implications of these results for energy dissipation mechanisms and relaxation dynamics in organic thin films are discussed and analogies to the properties of the so-called plastic-crystalline state are developed.