A process for preparing reactive polymers and polymers prepared by the foregoing process are disclosed. This process comprises polymerizing a monomer comprising at least one isopropenylphenyl glycidyl ether represented by formula (1): ##STR1## wherein all the symbols are defined in the appended claims, or in combination with at least one other unsaturated monomer, by the use of a catalyst selected from halogens and hydrogen iodide. The reactive polymer prepared by the above process is represented by the general formula (2): ##STR2## wherein all the symbols are defined in the appended claims, and has a number average molecular weight of 500 to 50,000.