Described is a method for imparting a substantive fragrance to fabrics being washed or dried in a washing machine or clothes dryer by means of tumbling the fabrics with one or more sachets, each of which contains fragrance-containing particles. The polymer particles comprise an ethylene-vinyl acetate copolymer, a blend of polyethylene and an ethylene/vinyl acetate copolymer, an ester-terminated polyamide, a blend of an ester-terminated polyamide and a polysaccharide and/or a C₁-C₄ alkyl methacrylate polymer. A method for producing fragrance-containing particles is also disclosed.