A number of solid peroxyacids are obtained by precipitation from a highly acidic reaction media in which they are prepared by sulphuric acid catalysed reaction of a corresponding carboxylic acid with hydrogen peroxide. The physical characteristics and purity of the precipitated solids are controlled by the method of precipitation. A product having a balance of acceptable filtration and washing rate with acceptable product purity is obtained by precipitating in the presence of a surfactant at a low concentration, such as in the range of from about 0.02 % to 0.5 % by weight, based on the weight of the diluted reaction mixture. The dilution process can be carried out in a single stage process, batchwise or continuously, or in a multi stage dilution process in which the first stage preferably dilutes to the point at or around when precipitation appears and is conducted rapidly, and subsequent dilution is conducted more slowly. Dilution can be conducted using water/ice, optionally containing to a lower concentration sulphuric acid and/or dilute hydrogen peroxide. The invention process is particularly suitable for the preparation of particulate poorly water-soluble diamidoperacids, including specifically terephthaloyl diamidoperoxycaproic acid of formula HO3C-(CH2)5-NH-CO-C6H4-CO-NH-(CH2)5-CO3H or the corresponding monoperacid, which can be obtained in a new crystalline form in the presence of sufficient surfactant. The invention process can be tailored to produce particulate peracid derivatives of phenylenediamidoalkylenecarboxylic acids having increased particle size, such as from 10 to 40 mu .