Liquid formulations of imidoalkanepercarboxylic acids, in the form of aqueous dispersions comprising, in percentages by weight relative to the total weight of the composition: A) from ≧7% to 40% and preferably from 10% to 20% of imidoalkanepercarboxylic acids having the general formula (I), the said imidoalkanepercarboxylic acids being in the β form and having a dissolution time, determined via the test of the rate of dissolution at a temperature of 40° C. or 18° C., of not more than 5 minutes when determined at 40° C. or 15 minutes when determined at 18° C., for an amount of dissolved acid equal to 99% of the theoretical amount; B) from 0.001% to 0.9% of a nonionic surfactant; the said dispersions having a viscosity of not more than 2000 mPa·sec at 25° C. by applying a shear rate of 20 s−1; in which the dissolution time of the component A), determined via the test of the rate of dissolution at a temperature of 40° C. or 18° C., is not more than 5 minutes when determined at 40° C. or 15 minutes when determined at 18° C., for an amount of dissolved acid equal to 99% of the theoretical amount, as defined in the rate of dissolution test; the said dispersions in the test of stability at 40° C. for seven days show variations in viscosity of not more than 300 mPa·sec; the said aqueous formulations being obtainable by grinding the crystals of imidoalkanepercarboxylic acids in α form dispersed in an excess of water, in the presence of a surfactant chosen from nonionic surfactants; cooling the liquid dispersion to a temperature below 30° C.