A process for the polymerization which comprises polymerizing batchwise at least one gaseous or super-critical fluorinated olefin monomer or a monomer mixture of the olefin monomer with other monomer copolymerizable with the olefin monomer in an aqueous medium while diffusing the olefin monomer or monomer mixture into the medium, wherein the quantity of the monomer or monomer mixture diffused in the medium prior to the polymerization is at least 80 % of the theoretical consumption of the monomer or monomer mixture which must be found if the polymerization occurs at a theoretical rate of polymerization. The process can attain a high rate of polymerization with the rate of polymerization being determined not by the diffusion of the monomeric gas.