Mono- and bis-hypofluorites respectively of formula: FO.sub.2 S--R.sub.f --CF.sub.2 OF and FOCF.sub.2 --R'.sub.f --CF.sub.2 OF wherein R.sub.f is perfluoroalkylene or perfluorochloroalkylene and R'.sub.f is a perfluoroalkylene or perfluorooxyalkylene, and process for preparing them, which is conducted continuously, at a temperature from 0.degree. to 60.degree. C. and comprises starting from the respective acyl fluorides ##STR1## by reaction of fluorine in the gas phase in the presence of a catalyst consisting of K, Rb, Cs or Ba fluoride, preferably supported on a metal material.