The process targets the removal of interfering materials from an aqueous fibrous material suspension, especially if this is produced from recycled paper. Thereby interfering materials, such as printing ink particles, small synthetic particles, or sticky contamination, are eliminated by flotation in a particularly advantageous manner. In accordance with the invention, the combination of low-intensity and high-intensity flotation is undertaken, whereby the low-intensity flotation generally works in the gravitational field and the high-intensity flotation in a centrifugal field.