A continuous process for producing ammonium sulfate crystals, wherein said process comprises: (a) feeding to a first group of crystallization sections, which crystallization sections are heat integrated in series, a first aqueous ammonium sulfate solution that contains one or more impurities; (b) feeding to a second group of crystallization sections, which crystallization sections are heat integrated in series, a second aqueous ammonium sulfate solution that contains one or more impurities; (c) crystallizing ammonium sulfate crystals in each crystallization section respectively from each of said solutions of ammonium sulfate that contain one or more impurities; (d) purging a fraction of the ammonium sulfate solution that contains one or more impurities from each of said crystallization sections; and (e) discharging ammonium sulfate crystals from each crystallization section, characterized in that: (i) both the first group of crystallization sections and the second group of crystallization sections are together heat integrated in one series of crystallization sections; wherein the first group of crystallization sections operates at higher temperature than the second group of crystallization sections; (ii) the composition of the first aqueous ammonium sulfate solution that contains one or more impurities is different to the composition of the second aqueous ammonium sulfate solution that contains one or more impurities; and (iii) the first aqueous ammonium sulfate solution that contains one or more impurities and the second aqueous ammonium sulfate solution that contains one or more impurities are each independently produced as a by-product during the production of cyclohexanone oxime, caprolactam or acrylonitrile. (a) feeding to a first group of crystallization sections, which crystallization sections are heat integrated in series, a first aqueous ammonium sulfate solution that contains one or more impurities; (b) feeding to a second group of crystallization sections, which crystallization sections are heat integrated in series, a second aqueous ammonium sulfate solution that contains one or more impurities; (c) crystallizing ammonium sulfate crystals in each crystallization section respectively from each of said solutions of ammonium sulfate that contain one or more impurities; (d) purging a fraction of the ammonium sulfate solution that contains one or more impurities from each of said crystallization sections; and (e) discharging ammonium sulfate crystals from each crystallization section, characterized in that: (i) both the first group of crystallization sections and the second group of crystallization sections are together heat integrated in one series of crystallization sections; wherein the first group of crystallization sections operates at higher temperature than the second group of crystallization sections; (ii) the composition of the first aqueous ammonium sulfate solution that contains one or more impurities is different to the composition of the second aqueous ammonium sulfate solution that contains one or more impurities; and (iii) the first aqueous ammonium sulfate solution that contains one or more impurities and the second aqueous ammonium sulfate solution that contains one or more impurities are each independently produced as a by-product during the production of cyclohexanone oxime, caprolactam or acrylonitrile. (i) both the first group of crystallization sections and the second group of crystallization sections are together heat integrated in one series of crystallization sections; wherein the first group of crystallization sections operates at higher temperature than the second group of crystallization sections; (ii) the composition of the first aqueous ammonium sulfate solution that contains one or more impurities is different to the composition of the second aqueous ammonium sulfate solution that contains one or more impurities; and (iii) the first aqueous ammonium sulfate solution that contains one or more impurities and the second aqueous ammonium sulfate solution that contains one or more impurities are each independently produced as a by-product during the production of cyclohexanone oxime, caprolactam or acrylonitrile.