Abstract: A process for washing a cellulose pulp from alkali digestion, wherein the pulp is fed into a multistage washing system comprising several countercurrently coupled washers, acid is added to a washing solution, the acidified fiber suspension is fed further to the following stage wherein the acidified solution is replaced in the fiber suspension by washing water, and the filtrate obtained from this stage is used after acidification at least partially as a washing solution at the previous stage. The acid is added at a stage when the concentration of the dissolved organic substances is at a value that detrimental precipitation of the organic substances is prevented.