A non-film forming, aqueous composition is disclosed for cleaning and for killing and inhibiting the regrowth of fungi and algae on a solid surface. The composition comprises a water-insoluble compound selected from the group consisting of a fungicide, an algicide and a mixture thereof dispersed in the composition, a detergent, a thickener, an oxidizing agent and water. Also disclosed is the composition in a two package form in which the oxidizing agent and at least a portion of the water are in one package, and the fungicide, algicide or mixture thereof, the detergent, the thickener, and optionally a portion of the water are in another package.Also disclosed is a process for cleaning a solid surface with the aqueous composition.