Process for preparing a polyvinylidenefluoride homopolymer having a head-to-head and tail-to-tail inversion content between 5 and 5.5% by mols, a yield point greater than 50 MPa and an elastic modulus greater than 1500 MPa (measured at 23.degree. C. according to ASTM D-1708 Method), a Melt Flow Index (MFI, measured at 230.degree. C. with a 5 kg load according to ASTM D-1238 Method) between 1 and 25 g/10', and thermal stability to dehydrofluorination consisting essentially of polymerizing vinylidene fluoride in aqueous emulsion in the presence of a non-hazardous organic peroxide selected from dialkylperoxides, dialkylperoxycarbonates, dibenzoylperoxide, t-alkylperoxybenzoates, and t-alkylperoxypivalates, having a self-accelerating decomposition temperature (SADT) greater than 50.degree. C. and of a chain transfer agent, at a temperature between 95.degree. and 120.degree. C. wherein said chain transfer agent is fed into the reactor continuously or in discrete amounts during the polymerization.