Laundry or cleaning composition comprising: a) an effective amount of a bleach activator and/or organic percarboxylic acid; b) a catalytically effective amount of a transition-metal bleach catalyst which is a complex of a transition-metal and a cross-bridged macropolycyclic ligand; and c) at least about 0.1% of one or more laundry or cleaning adjunct materials. Preferred compositions are laundry compositions and automatic dishwashing detergents which provide enhanced cleaning/bleaching benefits through the use of such catalysts in combination with bleach activators and/or organic perearboxylic acids.