Fig. 1 is a plan view of an apparatus for bleaching in accordance with this invention, comprising a series of four chests, and Fig. 2 is a vertical longitudinal section of a modified arrangement of two chests in line with one another, and with the conveyor for the material to be bleached and the passage through which said material passes from the top of one chest into the bottom of the next chest in the plane of section. [Illustration: Fig. 1] The chests, _a_ _a2_ _a3_ _a4_, may be of any desired shape and dimensions and any desired number may be used. Each of said chests is provided with an inlet passage, _b_, opening into the same near its bottom, and through this passage the materials are introduced. The unbleached material, which may be paper pulp or material which is readily held in suspension in a liquid and is capable of flowing or being conveyed from one point to another in a semi-fluid condition, is introduced through the inlet passage, _b_, to the first chest, _a_, of the series, said pulp preferably having had as much as possible of the liquid in which it was previously suspended removed without, however, drying it, and, together with the said pulp, the bleaching agent which has previously passed through the other chests of the series, as will be hereinafter described, is introduced so that both enter together at the lower portion of the first chest, _a_, of the series. The said materials are caused to flow into the chest continuously, so that the portion at each moment entering tends to displace that which has already entered, thus causing the materials to rise gradually or flow upward from the bottom to the top of the chest. Suitable stirring devices or agitators, _c_, may be employed to keep the pulp in suspension and to expose it thoroughly and uniformly to the liquid introduced with it. [Illustration: Fig. 2]