The spectra of thermal desorption (TDS spectra) of hydrogen isotopes from structural materials are investigated by various mathematical models, in particular, in the form of a first-order reaction for the volume-averaged concentration (in the case of limitation by diffusion), second-order models (taking into account the recombination of hydrogen atoms on the surface into molecules), and more detailed models reflecting multistage transport (diffusion in the bulk, migration to the surface, recombination, desorption). It is interesting to analyze the structure of the spectrum in order to identify the causes and «driving forces» of a physical and chemical nature corresponding to each peak. The article provides an analysis of some of the mentioned models for two-peak spectra and the results of numerical modeling.