To obtain a cross-linked polymer useful as an electrolytic material, useful for providing a photoelectrochemical battery using a photoelectric transfer element having excellent photoelectric transfer characteristics and durability by reacting a nitrogen-containing polymer compound with an electrophilic reagent.

This cross-linked polymer is obtained by reacting a nitrogen- containing polymer compound with a di- or polyfunctional electrophilic reagent. Preferably, the nitrogen-containing polymer compound has a repeating unit of the formula [R1 is H or a 1-4C alkyl; Z is a nitrogen-containing heterocyclic group; A is a repeating unit derived from an ethylenic unsaturated group- containing compound; (x) is 5-100 mol% and (y) is 0-95 mol%]. The nitrogen- containing polymer compound has preferably 2,000-100,000 weight-average molecular weight. The di- or polyfunctional electrophilic reagent is preferably selected from an alkyl bromide compound, an alkyl iodide compound, etc. The amount of the electrophilic reagent used is preferably 0.1-1 equivalent based on the number of mols of nitrogen atom to be reacted in the nitrogen-containing polymer.