Abstract: The invention relates to the preparation of dilute solutions of aliphatic rboxylic peracids.In a first step, a concentrated solution of aliphatic peracid is prepared from the corresponding acid or anhydride and concentrated hydrogen peroxide in the presence of a strong acid catalyst, preferably the minimum quantity necessary for obtaining equilibrium in the system within 48 hours; and in a second step, the concentrated solution of aliphatic peracid is diluted with a solution containing at least one of the reagents, so as to bring the concentration of aliphatic peracid to the rated concentration of the mixture.The method is applicable inter alia to the preparation of stable dilute solutions of peracetic acid.