PURPOSE: To obtain a cross-linked polymer useful as an absorbent, a water retaining agent, etc., having excellent chemical stability, liquid absorbing properties for an aqueous liquid or an alcohol, gel strength and economic efficiency by copolymerizing a specific N-vinylcarboxylic acid amide with an allyl compound or a vinyl ester compound.

CONSTITUTION: This cross-linked polymer is obtained by copolymerizing (A) an N--vinylcarboxylic acid amide of formula I (R1 and R2 are H or CH3) or a mixture of it and a monomer copolymerizable with it, (B) a compound containing two or more allyl groups in one molecule [e.g. a compound of the formula, (CH2=CH-CH2-)n)-Z ((n) is ≥2; Z is an nvalent organic group)] or (C) a compound containing two or more vinyl ester structures in one molecule [e.g. a compound of formula II ((m)≥2; Z' is an m-valent organic group)] and absorbs ≥10 times as much water as the empty weight.