The molecular dynamics of one monolayer adsorption species of di-tert-butyl nitroxide (DTBN) adsorbed on a thin film of gamma-Al2O3(111) grown on a NiAl(110) single crystal has been studied via ESR line-shape analysis. Below 200 K a rigid limit spectrum is found, above this temperature the changes in line shape are consistent with slow motions of the molecule. Best agreement between the experimental spectra and simulations is obtained using a "moderate jump" model with both Brownian diffusion and jump type contributions to the molecular dynamics. The motional processes have an activation energy of about 9 kJ/mol.