A method of operating a once-through steam generator having a first evaporator heating surface formed of a tube wall of a combustion chamber, and a second evaporator heating surface connected in parallel to the first evaporator heating surface at a water inlet side thereof, the second evaporator heating surface being located in a convection chamber post-connected to the combustion chamber at a flue-gas outlet side thereof downstream from a superheating surface as viewed in a flow direction of flue gas, includes opening a water regulating valve preconnected to the second evaporator heating surface in the flow direction of the feedwater, if a predetermined value of a mass flow of the feedwater into the once-through stem generator is exceeded, so as to initiate a partial mass flow of the feedwater into the second evaporator heating surface; and closing the water regulating valve again, if the predetermined value fails to be attained, so as to terminate the partial mass flow of the feedwater into the second evaporator heating surface.