The invention relates to novel polymers or oligomers containing at least sulfinate groups (P-(SO2)nX, X=1-(n=1), 2-(n=2) or 3-(n=3) valent metal cation or H+ or ammonium ion NR4+ where R=alkyl, aryl, H), which are obtained by completely or partially reducing polymers or oligomers containing at least SO2Y-groups (Y.dbd.F, Cl, Br, I, OR, NR2 (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 Polymer and polymer(blend)membranes which are obtained by further reacting the received 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.