Time-resolved surface-enhanced Raman spectroscopy (TRSERS) and potential-averaged surface-enhanced Raman spectroscopy (PASERS) have been combined with the potential step method to study thiourea (TU) and ClO4- coadsorbed at Ag electrodes. The SERS intensity-time profiles show that when a potential step is applied, the response rate of the SERS intensity depends significantly on the stepping direction. The slow surface process may involve a rearrangement of the coadsorbed layer which has two distinct structures at the two potentials stepped. Furthermore, the intensities of different SERS bands for the adsorbed TU have surprisingly different response rates to the potential step. This reveals that for detailed structural dynamic studies of some complicated electrosorption process it may be necessary to focus individually on various groups (or intramolecular bondings) of the adsorbate rather than considering the whole adsorbate as rigid, as is usually done.