This invention relates to a p-methyl styrene polymer represented by the following formula: ##STR1## Z denotes a group such as a functional group. Poly p-methylstyrene (PPMS) is lithiated by reaction with n-butyllithium. The lithiated PPMS is used to prepare polymers containing functional groups. As an example, a solution of PPMS (MW 260,000), 1.0 g in 20 ml of cyclohexane, was reacted with n-butyllithium, 8.5 mmol, and tetramethylethylenediamine, 8.7 mmol, for 20 hours to obtain a precipitate. The precipitate was dissolved in THF, and CO.sub.2 was blown into the solution. The solution was washed with an aqueous solution of HCl and dropped into methanol to obtain a solid polymer having carboxyl group functionality.