Abstract: A steam generator, in particular a waste-heat steam generator, includes first and second evaporator heating surfaces located in an elongate gas flue for hot gas. A first supply line for feed water is throughflow-connected on an inlet side to the first evaporator heating surface, while the second evaporator heating surface is throughflow-connected on an inlet and an outlet side to a low-pressure drum. The low-pressure drum is provided with a second supply line for feed water. The first supply line has a first treatment point and the second supply line a second treatment point. Each of the treatment points serves for adding and/or extracting chemicals for water treatment, so that each evaporator heating surface can receive only feed water which is conditioned according to regulations applying to that evaporator heating surface. A method for operating the steam generator is also provided.