A household laundry-drying machine comprising a drum rotatable about an axis of rotation and defining a laundry drying compartment, said drum comprising a substantially cylindrical peripheral wall which surrounds the laundry drying compartment, at least one laundry-agitation member associated to the cylindrical peripheral wall and protruding internally to the laundry drying compartment, an air heater for drying the laundry, and a conduit for conveying the air from the air heating means to the laundry drying compartment.The laundry-agitation member comprises a cavity in fluid communication with the laundry drying compartment, said cavity being suitable for containing at least one substance to be delivered in the laundry drying compartment during a drying cycle. The cavity of the laundry-agitation member is external to said means for conveying the air.