This invention relates to a process and an aqueous composition for killing spores. The process comprises contacting the spores with the aqueous composition for a sufficient period of time to effect a desired reduction (e.g., at least a 4 log reduction) in the number of spores capable of reproduction, metabolism and/or growth. The aqueous composition comprises water, peracetic acid and hydrogen peroxide. The concentration of peracetic acid in the water may be in the range from about 0.001 to about 60% by weight, or from about 0.001 to about 0.5% by weight. The weight ratio of peracetic acid to hydrogen peroxide may be in the range from about 0.001 to about 0.5.