The nonlocality property of the elastic channel optical potential is studied using a schematic coupled-channel system. It is explicitly shown that, consistent with the usual adiabatic approximation, the nonlocality is reduced as the scattering energy approaches the elastic threshold. The residual nonlocality found in the data may be partly due to the artificial truncation of the channels, and strong indications are found that a more complete treatment which includes a large number of channels would lead to better locality of the optical potential at low energy. For optical potentials corresponding to the inelastic channels, we find that the adiabaticity and the consequent locality is not well satisfied.