The apparatus forming the subject of this invention was designed by Francis A. Cloudman, Erwin B. Newcomb, and Frank H. Cloudman, of Cumberland Mills, Me., and comprises a series of tanks or chests, two or more in number, through which the material to be bleached is caused to pass, being transferred from one to the next of the series in order, while the bleaching agent is caused to pass through the series of chests in the reverse order, and thus acts first and at full strength upon the materials which have previously passed through all but the last one of the series of chests and have already been subjected to the bleaching agent of less strength. For convenience, the chest in which the material is first introduced will be called the "first of the series" and the rest numbered in the order in which the material is passed from one to the other, and it will be understood that any desired number may be used, two, however, being sufficient to carry on the process. The invention is shown embodied in an apparatus properly constructed for treating pulp used for the manufacture of paper, and for convenience the material to be bleached will be hereinafter referred to as the pulp, although it is obvious that similar apparatus might be used for bleaching other materials, although the apparatus might have to be modified to adapt it for conveying other materials of different nature than pulp from one bleaching chest to the other and for separating out the bleaching liquid and conveying it from one chest to the other in the reverse order to that in which the material passes from one chest to the next. The pulp material with which the apparatus herein illustrated is intended to be used is retained in suspension in the bleaching liquid and flows readily through ducts or passages provided for it in the apparatus in which the pulp to be bleached and the bleaching liquid are introduced together at the bottom of each chest and flow upward therethrough, while at the top of each chest there are two conveyors, one for carrying the pulp from one chest to the next in order, while the other carries the bleaching liquid from one tank to the next in the reverse order, the said conveyors also acting to partially separate the pulp from the liquid in which it has been suspended during its upward passage through the chest. Suitable agitators may be employed for thoroughly mixing the materials in the chest and in the apparatus shown the bleaching agent and material to be bleached pass through each chest in the same direction--namely from the bottom to the top--although they are carried from one chest to the next in the reverse order, the material to be bleached being primarily introduced into the chest at one end of the series, while the bleaching agent or solution is introduced primarily into the chest at the other end of the series.