Textile materials comprised at least partially of cotton are cleaned with a laundry detergent comprising bleach and an alkylated and/or hydroxyalkylated soil release-capable cellulose derivative having an average of from 0.5 to 2.5 alkyl groups and/or from 0.02 to 0.5 hydroxyalkyl groups per anhydroglycose monomer unit. The textile materials are cleaned more effectively with a laundry detergent containing the alkylated and/or hydroxyalkylated soil release-capable cellulose derivative.