The invention relates to a method of automatic dishwashing of dishware using wash water, in which, in a first step, a first composition, which comprises an oxygen bleach but substantially no enzyme, is supplied to the wash water, and the dishware is washed in a washing zone with the oxygen bleach-containing wash water; and, in a second step which occurs after the first step, a second composition, which comprises an enzyme but substantially no bleach, is supplied to the wash water, and the dishware is washed in said washing zone with the enzyme-containing wash water. The invention also relates to an automatic dishwasher and a cartridge suitable for use in this method.