Abstract: A method and apparatus provide for the bleaching of mechanical pulp in such a way that the brightness of the mechanical pulp can be increased up to about 7-10 points. Mechanical pulp directly from a secondary refiner is separated, as by first and second centrifugal separators (cyclones), into a fines fraction and a fiber fraction. The fines fraction is under about 200 mesh. The fiber fraction is mixed with hydrogen peroxide (H.sub.2 O.sub.2) and subjected to displacement bleaching, which uses a minimum about of bleaching chemical to obtain the maximum brightness. The fines fraction is mixed with hydrogen peroxide and subjected to non-displacement bleaching. The fines fraction is between about 10-20 percent of the total feed pulp stream. After bleaching, the fines and fiber streams can be recombined before passage to a paper products production machines.