To check the possibility of living polymerization with a biscyclopentadienyl metallocene, propylene polymerization was conducted by Cp2ZrMe2 at -78 degrees C or Cp2HfMe2 at -50 degrees C using B(C6F5)(3) and AlOct(3) as a cocatalyst. The polymer yield increased linearly with polymerization time. The polypropylene obtained showed narrow molecular weight distribution ((M) over bar(w)/(M) over bar(n) 1.04-1.15). In addition, the number-average molecular weight increased in proportion to the polymerization time. It was, thus, found that living polymerization of propylene proceeds with the catalyst systems at a very low temperature. Isospecific living polymerization of 1-hexene also proceeded with the rac-(et)Ind(2)ZrMe(2) catalyst at -78 degrees C.