Laundry or cleaning composition comprising: (a) an effective amount, preferably from about 0.0001% to about 99.9%, more typically from about 0.1% to about 25%, of a bleach activator and/or organic percarboxylic acid; (b) a catalytically effective amount, preferably from about 1 ppb to about 99.9%, 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, preferably comprising an oxygen bleaching agent. 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 percarboxylic acids.