The present invention relates to a process for removal or bleaching of soiling or stains present on cellulosic fabric, wherein the fabric is contacted in aqueous medium with a modified enzyme (enzyme hybrid) which comprises a catalytically active amino acid sequence of a non-cellulolytic enzyme linked to an amino acid sequence comprising a cellulose-binding domain. The invention further relates to a detergent composition comprising an enzyme hybrid of the type in question and a surfactant, and to a process for washing soiled or stained cellulosic fabric, wherein the fabric is washed in an aqueous medium to which is added such a detergent composition.