An apparatus and method permit continuous separation of an adsorbate from a processing material containing solid particles, sticky substances and water-soluble proteins, alone or in combination, without pretreatment. The processing is carried out while a loop adsorbent is circulated. An adsorbate is adsorbed, not by supply of the processing solution through the adsorbent, but by contact thereof with the adsorbent. In addition, the adsorbent after desorption of the adsorbate is cleaned. As a result, the apparatus and the method achieve continuous processing and separation of the adsorbate even from a processing material containing solid particles, sticky substances and water-soluble proteins alone or in combination without pretreatment.