NOVELTY - A crosslinked polybenzoxazines material comprises: a polymerization reaction product of a first benzoxazine monomer, second benzoxazine monomer, and crosslinkable compound.    USE - In the preparation of a electrolyte membrane which is used in a fuel cell (all claimed).    ADVANTAGE - The crosslinked polybenzoxazines material has improved has strong acid trapping capability, improved mechanical properties, and excellent chemical stability as it does not melt in polyphosphoric acid; improved phosphoric acid-containing capability at a high temperature. Even as the amount of impregnated proton carrier and the temperature are increased, mechanical and chemical stability is highly maintained, and thus the electrolyte membrane can be effectively used for fuel cells at a high temperature. The material provides fuel cell having improved efficiencies on fuel use and electric power generation.    DETAILED DESCRIPTION - A crosslinked polybenzoxazines material comprises: a polymerization reaction product of a first benzoxazine monomer of formula (I), a second benzoxazine monomer of formula (II), and crosslinkable compound.    R1=4-20C cycloalkyl (optionally substituted), T1, hydrogen atom, halo atom, OH or cyano;    T1=1-20C alkyl, 2-20C alkenyl, 2-20C alkynyl, 6-20C aryl, 2-20C heteroaryl, 2-20C heterocyclic (all optionally substituted);    R2=7-20C arylalkyl, 2-20C heteroarylalkyl, 4-20C carbocyclic group, 4-20C carbocyclicalkyl group, 2-20C heterocyclicalkyl group (all optionally substituted) or T1;    R3=1-20C alkylene, 2-20C alkenylene, 2-20C alkynylene, 6-20C arylene, 2-20C heteroarylene (all optionally substituted), -C(=O)- or -SO2-.    INDEPENDENT CLAIMS are included for the following:    (1) an electrolyte membrane comprising: the crosslinked material;    (2) preparation of the electrolyte membrane involving: mixing the first benzoxazine monomer, the second benzoxazine monomer, and the crosslinkable compound, curing the mixture to form a crosslinked material of polybenzoxazines, and impregnating the cured mixture with a proton conductor to form an electrolyte membrane;    (3) preparation (M2) of the electrolyte membrane involving: mixing the first benzoxazine monomer, the second benzoxazine monomer, and the crosslinkable compound, and forming a membrane using the mixture, curing the membrane; and impregnating the cured membrane with a proton conductor to form electrolyte membrane; and    (4) a fuel cell, comprising:an electrolyte membrane.