The experiments on the kinetics of molecular desorption from structurally disordered adsorbents clearly demonstrate its non-Debye behavior at “long” times. In due time, when analyzing the desorption of hydrogen molecules from crystalline adsorbents, attempts were made to associate this behavior with the manifestation of second-order effects, when the rate of desorption is limited by the rate of surface diffusion of hydrogen atoms with their subsequent association into molecules. However, the estimates made in the present work show that the dominance of second-order effects should be expected in the region of times significantly exceeding those where the kinetics of H2 desorption have long acquired a non-Debye character. To explain the observed regularities, an approach has been developed according to which frozen fluctuations in the activation energy of desorption play a crucial role in the non-Debye kinetics of the process. The obtained closed expression for the desorption rate has a transparent physical meaning and allows us to give a quantitative interpretation of a number of experiments on the desorption kinetics of molecules not only from crystalline (containing frozen defects) but also from amorphous adsorbents. The ways of further development of the proposed theory and its experimental verification are outlined.