To safely and simply obtain the subject compound useful as a developing agent for silver halide photographic photosensitive materials in a high yield by oxidizing a dialkylamine compound in the presence of a rhenium catalyst.

An N,N-dialkylhydroxyamine compound of formula I [R1, R2 are each a lower alkyl; (m), (n) are each 2-6] is synthesized by oxidizing a dialkylamine compound of formula II with hydrogen peroxide in a molar ratio of 0.5-1.5 in the presence of a Re catalyst (e.g. methyltrioxorhenium). The Re catalyst is used in an amount of 0.01-0.05mol.% based on the compound of formula II, and the reaction is carried at a reaction temperature of -10 to 40°C preferably for 5min to 15hr. The compound of formula I is not isolated and subsequently further reacted with a protonic acid in an amount of 0.7-1.2 moles per mole of the compound of formula II at a reaction temperature of -10 to 40°C preferably for 5min to 3hr to obtain the N,N-dialkylhydroxyamine compound protonic acid salt of formula III.