Abstract: The disclosure concerns a process and an apparatus for recovering fiber suspension from a mixture of different types of waste paper. The waste paper is disintegrated in a pulper to form a fiber suspension comprised of individual fibers. After perhaps passing a presorting device, the fiber suspension passes through a sorting device which separates the fibers into a long-fiber fraction and a short-fiber fraction. The two fractions are subsequently treated in different ways, generally for the purpose of cleaning the fiber fractions. Various treatment techniques are disclosed, including separating impurities from the long-fiber fraction by flotation and/or bleaching the long-fiber fraction and washing the short-fiber fraction and/or treating it by flotation for de-inking the short-fiber fraction and perhaps thereafter sorting the short-fiber fraction to remove impurities.