Abstract: Bleaching of cellulose pulp with peroxide is accomplished and has the advantages of conventional pressurized peroxide bleaching without the need for a large pressurized vessel. Pulp at a consistency of between about 8-20% is mixed with peroxide and introduced into a first relatively-small treatment vessel where it is held at a pressure of between about 3-20 bar, and is treated for between 10-60 minutes. Pulp reacts with the peroxide so that there is less than 5 kg of hydrogen peroxide per ton of pulp remaining, and then between about 40-90% of the gas is separated from the pulp at or adjacent discharge of the pulp from the first vessel. The pulp is then passed to a second substantially-unpressurized bleaching tower having an interior volume at least about twice as great as the first vessel. The pulp is introduced into the bottom of the second vessel and flows upwardly in it and is discharged from adjacent the top of the second vessel.