PROBLEM TO BE SOLVED: To provide a method of sterilizing a pure water production apparatus for pharmaceuticals capable of improving the hot water sterilizing efficiency and of ultimately inhibiting effects exerted onto an electric deionizer at the time of a hot water sterilizing treatment and a pure water production apparatus for pharmaceuticals.SOLUTION: In a provided method of sterilizing a pure water production apparatus furnished not only with a rotation frequency-variable pump, a heat exchanger, a reverse osmotic membrane device, and an electric deionizer in proper order along a treatment line connecting a raw water tank and a pure water tank or use point but also with circulatory lines connecting, to the raw water tank via ON-OFF valves, a concentrated water pipeline for the reverse osmotic membrane device, concentrated water and electrolyzed water pipelines for the electric deionizer, and a treated water pipeline for the electric deionizer, an aperture-variable valve is configured to interpose within the concentrated water pipeline, and the aperture of the aperture-variable valve is determined so as to realize, while hot water is being circulated through the treatment line and the circulatory lines, at least a prescribed value of the ratio, with respect to the permeated water flow rate of the reverse osmotic membrane device, of the concentrated water flow rate (C/P).