The invention relates to novel polymers or oligomers containing at least sulfonite groups (P--(SO.sub.2).sub.nX, X=1-(n=1), 2-(n=2) or 3-(n=3) valent metal cation or H.sup.+ or ammonium ion NR.sub.4.sup.+ where R=alkyl, aryl, H), which are obtained by completely or partially reducing polymers or oligomers containing at least SO.sub.2Y-groups (Y.dbd.F, Cl, Br, I, OR, NR.sub.2 (R=alkyl and/or aryl and/or H), N-imidazolyl, N-pyrazolyl) by means of suitable reducing agents in a suspension or in a solution form. The invention also relates to polymers and polymer(blend) membranes which are obtained by further reacting the obtained sulfinated polymers, especially by alkylation of the sulfinate groups with mono- di- or oligo functional electrophiles. The invention further relates to methods for producing the sulfinated polymers and for further reacting the sulfinated polymers with electrophiles by S-alkylation.