PURPOSE: To produce a polymer having improved resistance to deterioration due to heat and shear, by treating an anionic polymerization reaction mixture obtained by a specified method with a specified neutralizing agent.

CONSTITUTION: This polymer is produced by a process comprising the step (A) of bringing an anionically polymerizable monomer selected from aromatic monovilylidene monomers and alkadienes into contact with an anionic initiator containing an alkali metal under anionic polymerization conditions, the step (B) of bringing the reaction mixture into contact with a hydroxylated compound of the formula R-(OH)n (wherein R is a 10C or lower aromatic or aliphatic group; and n is 1 or 2) to terminate polymerization, the step (C) of bringing the reaction product into contact with an organic acid halide to neutralize the remnant containing an alkali metal and produced from the termination reaction in the step B, and the step (D) of recovering the produced polymer.