NOVELTY - An electrolyte has fluorine-containing cyclic structure and sulfonimide structure in principal chain or side chain. The fluorine-containing cyclic structure whose number of constituent atoms in ring is 3-8. The constituent atom of the ring consists of 2 or more oxygen atoms and 2 or more carbon atoms, where 2 or more of oxygen atoms are not bonded consecutively. The substituent on the carbon is fluorine or 1-10C perfluoroalkyl group optionally including ether bond and/or sulfonyl bond. Bridging is not included in the ring.    USE - Electrolyte is used for fuel cell (claimed). Uses include but are not limited to electrolytic membrane for electrolysis apparatus, hydrohalic acid electrolyzer, brine-electrolysis apparatus, oxygen and/or hydrogen concentrator, humidity sensor, and gas sensor, and catalyst layer ionomer.    ADVANTAGE - The electrolyte has excellent oxygen permeability, proton conductivity, water-repellent property and flexibility.    DETAILED DESCRIPTION - An electrolyte has fluorine-containing cyclic structure and sulfonimide structure in principal chain or side chain. The fluorine-containing cyclic structure whose number of constituent atoms in ring is 3-8. The constituent atom of the ring consists of 2 or more oxygen atoms and 2 or more carbon atoms, where 2 or more of oxygen atoms are not bonded consecutively. The substituent on the carbon is fluorine or 1-10C perfluoroalkyl group optionally including ether bond and/or sulfonyl bond. Bridging is not included in the ring. The sulfonimide structure is of formula: -(SO2NMSO2-(CRf5Rf6)k)a-SO2NMSO2- (I).    M=H or alkali metal;    Rf5,Rf6=fluorine or 1-10C perfluoroalkyl including ether bond and/or sulfonyl bond;    a=0-100;and    k=1-20.    INDEPENDENT CLAIMS are included for the following:    (1) fluorine-containing cyclic compound of formula: XO2S-P'-(CRf7Rf8)m-(SO2NMSO2-(CRf5Rf6)k)a-SO2X (III);    (2) fluorine-containing sulfonimide compound of formula: XO2S-(CRf7Rf8)m'-(SO2NMSO2-(CRf5Rf6)k)a-SO2X (IV);    (3) fluorine-containing cyclic compound precursor with structure of formula: Y'-P'-(CRf7Rf8)m-(SO2NMSO2-(CRf5Rf6)k)a-SO2X (V);    (4) manufacture of fluorine-containing cyclic compound precursor, which involves reacting fluorine-containing sulfonimide compound of formula: Y'-(CRf7Rf8)m'-(SO2NMSO2-(CRf5Rf6)k)a-SO2X (VI) and fluorine-containing carbocyclic-ring carbon double bond compound of formula (VII, VIII, IX and/or X); and    (5) manufacture of electrolyte, which involves reacting fluorine-containing cyclic compound (III) and fluorine-containing sulfonimide compound (IV).    P'=group of formula (i)-(iv);    Rf1-Rf8=fluorine or 1-10C perfluoroalkyl including ether bond and/or sulfonyl bond;    n=1 or more;    m=0-20;    X=halo or NH2;    m'=1-20;and    Y'=halo other than fluoro.