A cleaning composition with a bleaching and disinfecting action, consisting of peroxide bleach, corresponding bleach activator and substances assisting the cleansing action is described. High bleach concentrations are stabilised in the presence of a bleach activator by the dust-like portions of the bleach being taken up in the pores of a basic detergent. The cleaning composition can be used both directly on the textile fabric and as additive to wash liquors with conventional detergents, especially those without a bleaching system, even at temperatures from 20 DEG C.