In frozen biological media and molecular glasses only restricted motions exist; because of the weakness and disorder of intermolecular bonds these motions may have stochastic nature. Electron spin echo (ESE) spectroscopy of spin-labeled molecules allows detecting their restricted stochastic rotations (stochastic molecular librations). As in molecular disordered media motions may be highly cooperative, it would be desirable to investigate their spectroscopic manifestation also in the systems where cooperative effects would be certainly ruled out. In this work, ESE of spin-labeled molecules adsorbed on inorganic SiO2 surface was investigated in a wide temperature range. The rate of motion-induced spin relaxation was found to become measurable above 130 K, increasing with temperature and attaining then a saturating behavior with a well-defined maximum near 250 K. For two types of molecules differing remarkably in their size and polarity (a small highly-polar nitroxide radical and a large spin-labeled peptide), quite similar results were obtained. This saturating behavior was quantitatively reproduced in simulations within a simple model of jump between two close orientations. Comparison with experiment allowed estimate that at 250 K the correlation time of the motion τc is of the order of several tens of nanoseconds and the angle α between two orientations is around 0.02 rad. As the found saturating behavior is a property of individual motions, for any other molecular system an excess of the spin relaxation rate above the maximum found here for adsorbed molecules may be ascribed to cooperative motions. Comparison with literature data on molecular systems of different origin has shown that effects of cooperativity indeed are present and, moreover, may be very essential.