The invention relates to catalytically bleaching substrates, especially laundry fabrics, with atmospheric oxygen and a peroxyl species. A method of bleaching a substrate is provided that comprises applying to the substrate, in an aqueous medium, a specified organic substance which forms a complex with a transition metal, the complex catalysing bleaching of the substrate by atmospheric oxygen and a peroxyl species. Also provided is a bleaching composition comprising, in an aqueous medium, atmospheric oxygen and an organic substance which forms a complex with a transition metal, the complex catalysing bleaching of the substrate by the atmospheric oxygen, wherein the aqueous medium is provided with a peroxygen bleach or a peroxy-based or peroxy-generating bleach system.