A process is provided for the manufacture of fluoralkyliodides of high molecular weight from the corresponding perfluoralkyliodides of lower molecular weight. In this process a perfluoralkyliodide is telomerized with a perfluorethylene or a perfluorpropylene each optionally containing at most one chlorine atom, and an amine, in the presence of a metal salt of a metal of groups IIIa, IIIb to VIIIb of the 4th to 6th period or of groups Ia or IIa of the Period Table as a catalyst at 0.degree. to 350.degree. C and under a pressure from 0 to 200 atmospheres (gauge).The so-obtained products are useful as intermediates for the manufacture of carboxylic acids or alcohols or for reaction with non-fluoro compounds. The products thus obtained may be used as agents for conferring oleophobic or hydrophobic proerties, as soil release agents or also as hydraulic fluids.