The Perey-Buck effect is studied by comparing wave functions of non-local potentials with those of phase-equivalent local potentials which are energy independent. It is found that the Perey-Buck effect is true only for a restricted class of non-local potentials. Not only is it necessary that the extension of the non-locality be small, but also that the non-local potential obey a stringent condition such as the separability in the sum and difference of the coordinates, as assumed by Perey and Buck and by Austern.